Texas Go Math

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Unit 5 Study Guide Review Answer Key.

Texas Go Math Grade 7 Unit 5 Study Guide Review Answer Key

Applications of Geometry Concepts

Essential Question
How can you apply geometry concepts to solve real-world problems?

Example 1
Find (a) the value of x and (b) the measure of ∠APY.
a. ∠XPB and ∠YPB are supplementary.
3x + 78° = 180°
3x = 102°
x = 34°

b. ∠APY and ∠XPB are vertical angles,
m∠APY = m∠XPB = 3x = 102°

Example 2
Find the area of the composite figure. It consists of a semicircle and a rectangle.

Area of semicircle = o.5(πr²)
≈ 0.5(3.14)25
≈ 39.25 cm²
Area of rectangle = lw
= 10(6)
= 60 cm²
The area of the composite figure is approximately 99.25 square centimeters.

Texas Go Math Grade 7 Unit 5 Exercises Answer Key

Question 1.
Find the value of y and the measure of ∠YPS (Lesson 9.1)

Answer:
Angle on the straight line SPR will be 180° and the ∠YPS and YPR will be supplementary to each other so, the
sum of both angle will be 180°.
∠YPS + ∠YPR = 180°
∠YPS + 140° = 180
∠YPS = 180 – 140
∠YPS = 40°
Also ∠YPS and ∠RPZ are vertically opposite angle so both the angle will be equal in measure.
∠RPZ = ∠YPS
5y = 40°
y = \(\frac{40}{5}\)
y = 8°
∠YPS = 40°

Find the circumference and area of each circle. Round to the nearest hundredth. (Lessons 9.2, 9.3)

Unit 5 End of Unit Assessment Answer Key Grade 7 Question 2.

Answer:
Given diameter of the circle = 22 inch
Circumference of circle with diameter “D” is = πD
Circumference of circle = 22 . π
= 22 × 3.14 (π = 3.14)
≈ 69 inch
Area of circle with diameter “D” is = \(\frac{\pi D^{2}}{4}\)
Area of circle = \(\frac{\pi \cdot 22^{2}}{4}\)
= \(\frac{3.14 \times 484}{4}\)
≈ 380 inch²
Circumference is 69 inch and area is 380 inch²

Question 3.

Answer:
Given radius of the circle = 4.5 m
Circumference of circle with radius “r” is = 2πr
Circumference of circle = 2π × 4.5
= 9 × 3.14 (π = 3.14)
= 28.26 m
Area of circle with radius “r” is = πr²
Area of circle = π × 45²
= 3.24 × 20.25 (π = 3.14)
= 65.61 m²
Circumference is 28.26 m and area is 65.61 m².

Find the area of each composite figure. Round to the nearest hundredth if necessary. (Lesson 9.4)

Question 4.

Answer:
Side length of the square = 9 in
Height of the triangle = 9 in
Base of the triangle = 13 – 9 = 4 in
Area of the composite figure will be the sum of area of square and the triangle.
Area of square = side²
= 9² in²
= 81 in²

Area of triangle = \(\frac{1}{2}\) × Base × Height
= \(\frac{1}{2}\) × 4 × 9 in²
= 18 in²
Area of composite figure = Sum of area of square and triangle
= 81 + 18 in²
= 99 in²
Hence, area of the composite figure will be 99 in².
Area of the composite figure will be 99 in²

Question 5.

Answer:
Length ot the rectangle = 20 cm
Width of the rectangle = 16 cm
Radius of the semi circle = \(\frac{16}{2}\) = 8 cm
Area of the composite figure will be the sum of area of rectangle and the semi circle.
Area of rectangle = Length × width
= 16 × 20 in²
= 320 in²

Area of composite figure = Sum of area of rectangle and semi circle
= 320 + 100.18 cm²
≈ 420 cm²
Hence, area of the composite figure will be 420 cm².

Volume and Surface Area

Example
The height of the figure whose net is shown is 8 feet. Identify the figure. Then find its volume, lateral area, and total surface area.
The figure is a rectangular pyramid.

The volume of the rectangular pyramid is 384 cubic feet, the lateral surface area is 192 square feet, and the total
surface area is 336 square feet.

Exercises

7th Grade Unit 5 Study Guide Answer Key Question 1.
Identify the figure represented by the net. Then find its lateral area and total surface area. (Less0n 10.3)

Answer:
The figure represented by the net is a triangular prism.
Lateral area:
One 13 ft. by 10 ft rectangle;
Two 13 ft by 13 ft. rectangles.
1 . (13 . 10) = 130
2 . (13 . 13) = 338
Lateral area: 130 + 338 = 468 ft².
The base has the shape of triangLe with lenght of 10 ft and height of 15 ft.
Base area:
2 . (\(\frac{1}{2}\) . 10 . 15) = 150 ft²
The total surface area is 468 + 150 = 618 ft².

Lateral area: 468 ft².
The total surface area is 618 ft².

Find the volume of each figure. (Lessons 10.1,10.2)

Question 2.

Answer:
l = 7 in Length of base
w = 5 in Width of base
h = 12 in Height of a prism
Find the area of the base B. A prism has a base that is rectanguar, so use the formula:
B = l . w = 7 . 5 = 35 in²
Use the formula for the volume of a rectangular prism.
V = B . h = 35 . 12 = 420 in³
The volume of a rectangular prism is 420 in³.

Question 3.

Answer:
A pyramid has a base that is right triangle.
a = 4 m Length of one side of the triangle
b = 6 m Length of other side of the triangle
h = 9m Heightofapyramid
Find the area of the base B.

Use the formula.
V = B . h = 12 . 9 = 108 m³

The volume of a triangular pyramid is V = 108 m³.

Question 4.
The volume of a rectangular pyramid is 1.32 cubic inches. The height of the pyramid is 1.1 inches and the length of the base is 1.2 inches. Find the width of the base of the pyramid. (Lesson 10.1) _____
Answer:
V = 1.32 in³ The volume of a rectangular pyramid
h = 1.1 in Length of pyramid
1 = 1.2 in Length of base
w = ? Width of base

Use the formula for the volume of a pyramid to find a width of the base.
V = \(\frac{1}{3}\) . l . w . h
1.32 = \(\frac{1}{3}\) . (1.2) . w . (1.1)
1.32 = \(\frac{1}{3}\) . (1.32) . w

The width of the base of the pyramid is w = 3 in

Mathematics Grade 7 Unit 5 Test Study Guide Answer Key Question 5.
The volume of a triangular prism is 264 cubic feet. The area of the base of the prism is 48 square feet. Find the height of the prism.
(Lesson 10.2) ____
Answer:
V = B . h
B = 48 ft² Base of prism
h =? Height of a prism
V = 264 ft³ The volume of a prism
Use the formula for the volume of a prism to find the height of the prism.
V = B . h
264 = 48 . h
Divide both sides by 48.

The height of the prism is h = 5.5 ft.

Texas Go Math Grade 7 Unit 5 Performance Tasks Answer Key

Question 1.
Careers In Math Product Design Engineer Miranda is a product design engineer working for a sporting goods company. She designs a tent in the shape of a triangular prism. The dimensions of the tent are shown in the diagram.

a. Draw a net of the triangular prism and label the dimensions.

Answer:
The net of the given tent is a triangular prism.

b. How many square feet of material does Miranda need to make the tent (including the floor)? Show your work.
Answer:
Determine the surface area of the tent or the triangular prism:
SA = 3R + 2T
SA = 3(9.5 .8) + 2 (\(\frac{4 \cdot 6}{2}\))
SA = 3(76) + 2(12)
SA = 228 + 24
SA = 252 ft²

c. What is the volume of the tent? Show your work.
Answer:
Determine the volume of the tent or triangular prism.
V = B . h
= \(\frac{4 \cdot 6}{2}\) . 5
= 12 . 9.5
= 114 ft³

d. Suppose Miranda wants to increase the volume of the tent by 10%. The specifications for the height (6 feet) and the width (8 feet) must stay the same. How can Miranda meet this new requirement? Explain.
Answer:
The new volume of the tent is:
1.1V = 1.1 . 114 = 125.4 ft³.
The length of the tent, or the height of the prism h is the parameter being changed, so:
V = B . h

The tent will get longer by 10.45 – 9.5 = 0.95 ft.

Grade 7 Maths Geometry Unit 5 Test Answer Key Question 2.
Li is making a stand to display a sculpture made in art class. The stand will be 45 centimeters wide, 25 centimeters long, and 1.2 meters high.

a. What is the volume of the stand? Write your answer in cubic centimeters.
Answer:
The stand is in the form of a rectangular prism, whose volume is calculated by
V = length . width . height
Since 1.2 m = 120 cm, the volume of the stand is
V = l . w . h Write the formula for the volume
V = 45. 25. 120 Substitute the values
V = 135,000 cm³ Multiply the values

b. Li needs to fill the stand with sand so that it is heavy and stable. Each piece of wood is 1 centimeter thick. The boards are put together as shown in the figure, which is not drawn to scale. How many cubic centimeters of sand does she need to fill the stand? Explain how you found your answer.

Answer:
Determine the volume of the interior of the stand. To obtain that we have to “remove” 2 cm from each dimension,
thus length will be 43 cm, width is 23 cm and height is 118 cm.
V = l . w . h Write the formula for the volume
V = 43 . 23 . 118 Substitute the new values
V = 116, 702 cm³ Multiply the values

Texas Go Math Grade 7 Unit 5 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1.
The dimensions of the pyramid are given in centimeters (cm). What is the volume of the pyramid?

(A) 222.5 cubic centimeters
(B) 330 cubic centimeters
(C) 445 cubic centimeters
(D) 990 cubic centimeters
Answer:
(B) 330 cubic centimeters

Explanation:
h = 11 cm Height of pyramid
l = 9 cm Length of base
w = 10 cm Width of base
Use the formula for the voLume of a rectangular pyramid
V = \(\frac{1}{3}\) . l . w . h
= \(\frac{1}{3}\) . 9 . 10 . 11
= \(\frac{1}{3}\) . 990
= 330 cm³
The volume of the pyramid is 330 cm³

Question 2.
The volume of a triangular pyramid is 437 cubic units. The height of the pyramid is 23 units. What is the area of the base of the pyramid?
(A) 6.3 square units
(B) 19 square units
(C) 38 square units
(D) 57 square units
Answer:
(D) 57 square units

Explanation:
Use formula for the volume of a triangular pyramid.
B = ? Base of pyramid
h = 23units Height of a pyramid
V = 437 cubic units The volume of a pyramid
Use the formula for the volume of a pyramid to find a base area of the pyramid.
V = \(\frac{1}{3}\) . B . h
437 = \(\frac{1}{3}\) . B . 23
437 = (7.66) . B
Divide both sides by 7.66.

The area of the base of a pyramid is 57 square units.

Hot Tip!
Make sure you look at all the answer choices before making your decision. Try substituting each answer choice into the problem if you are unsure of the answer.

Question 3.
What is the lateral surface area of the square pyramid whose net is shown?

(A) 216 square feet
(B) 388 square feet
(C) 568 square feet
(D) 776 square feet
Answer:
(A) 216 square feet

Explanation:
Lateral surface area of square pyramid will be the sum of areas of all the triangles except base in the given figure.
Base of the triangle = 12 ft
Height of the triangle = 9 ft
We know that area of the rectangle is = \(\frac{1}{2}\) × Base × Height
Area of triangle = \(\frac{1}{2}\) × 12 × 9
= 54 ft²
Lateral surface area of pyramid = 4 × Area of triangle
= 4 × 54
= 216 ft²
Hence, lateral surface area is 216 ft² and option A is correct answer

Question 4.
A one-topping pizza costs $15.00. Each additional topping costs $1.25. Let x be the number of additional toppings. You have $20 to spend. Which equation can you solve to find the number of additional toppings you can get on your pizza?
(A) 15x + 1.25 = 20
(B) 1.25x + 15 = 20
(C) 15x – 1.25 = 20
(D) 1.25x – 15 = 20
Answer:
(B) 1.25x + 15 = 20

Explanation:
Given the cost of one-topping pizza = $13.00
The cost of additional topping on pizza = $1.25
It is given we have to spend only $20 on pizza. For “x” the number of additional topping cost will be 1.25 × x and the cost of one topping pizza will be $13. So the total cost of pizza will be the sum of cost. of one-topping pizza and the additional topping cost which will be equal to $20.
In form of equation: 1.25x + 15 = 20
Hence, option B is the correct answer.

Unit 5 Test Study Guide Geometry Basics Answer Key Question 5.
A bank offers a home improvement loan with simple interest at an annual rate of 12%. J.T. borrows $ 14,000 over a period of 3 years. How much will he pay back altogether?
(A) $15,680
(B) $17,360
(C) $19,040
(D) $20,720
Answer:
(C) $19,040

Explanation:
The principal amount of home loan (P) = $14. 000
Rate of the simple interest annually (r) = 12%
Duration for which loan is taken (t) = 3 years
We know that simple interest = \(\frac{P \times r \times t}{100}\)
Simple interest = \(\frac{14,000 \times 12 \times 3}{100}\)
= 140 × 36
= $5,040
Total which has to be paid = Principal Simple interest
= 14,000 + 5,040
= $19,040
Hence, option C is correct answer.

Question 6.
What is the volume of a triangular prism that is 75 centimeters long and that has a base with an area of 30 square centimeters?
(A) 2.5 cubic centimeters
(B) 750 cubic centimeters
(C) 1,125 cubic centimeters
(D) 2,250 cubic centimeters
Answer:
(D) 2,250 cubic centimeters

Explanation:
B = 30 cm² Base of prism
h = 75 cm Height of a prism
Use the formula for the volume of the prism.
V = B . h
= 30 . 75
= 2250 cm³

The volume of a triangular prism is 2250 cubic centimeters.

Question 7.
The radius of the circle is given in meters. What is the circumference of the circle? Use 3.14 for π.

(A) 25.12 meters
(B) 50.24 meters
(C) 200.96 meters
(D) 803.84 meters
Answer:
(B) 50.24 meters

Explanation:
Given radius of the circle (r) = 8 m
We know that circumference of circle of radius “r” is = 2πr
Circumference of circle = 2π × 8
= 16π
(π = 3.14)
= 16 × 3.14
= 50.24 meters.
hence, option B is correct answer.

Question 8.
The dimensions of the figure are given in millimeters. What is the area of the two-dimensional figure?

(A) 39 square millimeters
(B) 169 square millimeters
(C) 208 square millimeters
(D) 247 square millimeters
Answer:
(C) 208 square millimeters

Explanation:
The area of the two-dimensional figure has one 13mm. by 13 mm. square and one triangle with length of 13 mm. and height of 6 mm.
The area of the two-dimensional figure is:
(13 . 13) + (\(\frac{1}{2}\) . 13 . 6) = 169 + 39 = 208 mm²

The area of the two-dimensional figure is 208 square millimeters.

Gridded Response

Question 9.
What is the measure in degrees of an angle that is supplementary to a 74° angle?

Answer:
Supplementary angle : supplementary angle means the pair of angle whose sum is 180°.
Given angle in problem: = 74°
Let the other supplementary angle be = x°
x° + 74° = 180°
x = 180° – 74°
r = 106°
Hence, other supplementary angle wilt be 106°
Steps to plot the given box are:
In 1^st column : mark ‘+’ sign
In 2^nd column : mark “0”
In 3^rd column : mark “1”
In 4^th column : mark “0”
In 5^th column : mark “6”
In 6^th column: mark “0”
In 7^th column : mark “0”
106°

Question 10.
What is the volume in cubic centimeters of a rectangular prism that has a length of 6.2 centimeters, a width of 3.5 centimeters, and a height of 10 centimeters?

Answer:
Given length of the rectangular prism = 6.2 cm
Given width of the rectangular prism = 3.5 cm
Given height of the rectangular prism = 10 cm
Volume of rectangular prism = length × width × height
Volume of rectangular prism = 6.2 × 3.5 × 10
= 6.2 × 35
= 217 cm³
Hence, volume of the rectangular prism is 217 cm³.

Steps to plot the given box are:
In 1^st column : mark ‘+’ sign
In 2^nd column : mark “0”
In 3^rd column : mark “2”
In 4^th column : mark “1”
In 5^th column : mark “7”
In 6^th column: mark “0”
In 7^th column : mark “0”
volume of the rectangular prism is 217 cm³.

Hot Tip!
It is helpful to draw or redraw a figure. Answers to geometry problems may become clearer as you redraw the figure.

Geometry Unit 5 Review Answer Key Grade 7 Question 11.
What is the area of the circle in square meters? Use 3.14 for π.

Answer:
Given diameter of the circle (D) = 18 m
We know that area of circle of diameter “D” is = \(\frac{\pi D^{2}}{4}\)

hence, option B is the correct answer.

Steps to plot the given box are:
In 1^st column : mark ‘+’ sign
In 2^nd column : mark “0”
In 3^rd column : mark “2”
In 4^th column : mark “5”
In 5^th column : mark “4”
In 6^th column: mark “3”
In 7^th column : mark “4”
Area of circle is 254.34 m²

Texas Go Math Grade 7 Unit 5 Vocabulary Preview Answer Key

Use the puzzle to preview key vocabulary from this unit. Unscramble the circled letters to answer the riddle at the bottom of the page.

Question 1.
NEONGTURC LANSEG

Answer:

Question 2.
LEOTECRAYMPMN SEGLAN

Answer:

Question 3.
RIMEUCEEFNRCC

Answer:

Question 4.
LEARATL ERAA

Answer:

Question 5.
PIECOTMOS GUISEFR

Answer:

1. Angles that have the same measure. (Lesson 9.1) .
2. Two angles whose measures have a sum of 90 degrees. (Lesson 9.1)
3. The distance around a circle. (Lesson 9.4)
4. The sum of the areas of the lateral faces of a prism. (Lesson 10.3) .
5. A two-dimensional figure made from two or more geometric figures. (Lesson 9.4)

Q: What do you say when you see an empty parrot cage?
A: __ __ __ ___ __ __ ___ !

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 11.1 Answer Key Analyzing Categorical Data.

Texas Go Math Grade 7 Lesson 11.1 Answer Key Analyzing Categorical Data

Texas Go Math Grade 7 Lesson 11.1 Explore Activity Answer Key  

Solving Problems Involving Bar Graphs

The students in a class were surveyed to find out how many people live in their households. Household members might include parents, step parents, guardians, and siblings, as well as extended family, such as grandparents. The results of the survey are shown in the dot plot.

A. How many students were surveyed? How do you know?

B. What percent of the class has a household of 3 or fewer people?

Reflect

Go Math Lesson 11.1 Analyzing Categorical Data 7th Grade Question 1.
Critical Thinking What percent of households with 4 or fewer people have exactly 2 people?
Answer:
Total number family with 4 or fewer people = 15
Number of families with exactly two people = 3

Hence, 20% of family have exactly 2 people among family having 4 or fewer people.

Example 1.
Three boys and three girls ran for 7th grade class president. The boys are Andrew, Derrick, and Miguel. The girls are Becky, Dora, and Trisha. The results of the election are shown in the bar graph. Which is greater – the percent of total votes for boys that Derrick received, or the percent of total votes for girls that Dora received?

Step 1:
Calculate the percent of total votes for boys that Derrick received. Set up a ratio:

Derrick received 45% of the total votes for boys.
Step 2:
Calculate the percent of total votes for girls that Dora received. Set up a ratio:

Dora received 40% of the total votes for girls.
Step 3
Compare the percents calculated in the previous two steps.
Because 45% is greater than 40%, the percent of votes for boys that Derrick received is greater.

Your Turn

Question 2.
In Example 1, Calculate the percent of total votes that Dora received.
Answer:
Calculate the percent of total votes that Dora received.

Dora received 22.2% of the total votes for all canditates.

Example 2.
There are 5,000 tickets available for a concert. The percent of available tickets belonging to each ticket type is shown in the circle graph. Calculate the number of tickets available for each type of ticket.

Step 1
Write a ratio to represent each type of ticket.
Floor: 16% = \(\frac{16}{100}\)
Lower level: 30% = \(\frac{30}{100}\)
Platinum: 2% = \(\frac{2}{100}\)
Upper level: 44% = \(\frac{44}{100}\)
Club: 8% = \(\frac{8}{100}\)
Step 2:
Set up and solve a proportion to find the number of each type of ticket.

The floor has 800 tickets, the lower level has 1,500, the upper level has 2,200, the club has 400, and the platinum section has 100.

Your Turn

Texas Go Math Grade 7 Practice and Homework Lesson 11.1 Answer Key Question 3.
What percentage of sold tickets not on the floor were platinum tickets? Round to the nearest percent.
Answer:
Total number of tickets for concert = 5,000
Number of Platinum tickets = 100
Number of tickets on floor = 800
Number of non-floor ticket = 5,000 – 800 = 4,200
% of platinum ticket which are not on floor = \(\frac{100}{4200}\) × 100
= \(\frac{100}{42}\)
= 2.38%
Hence, 2.38% of non-floor tickets were platinum tickets.

Texas Go Math Grade 7 Lesson 11.1 Guided Practice Answer Key

Question 1.
The students in the class were asked which hand they preferred to use for writing. The bar graph shows the results. Of the students who had a preference, what percent chose the left hand? (Example 1)

Step 1
Find the total number of students who had a preference.
Left ___ Right ___ Total ____
Step 2:
Set up a proportion and find the percent.
________
Answer:
Left = 6
Right = 18
Total = 6 + 18 = 24

Hence, 25% of students have left hand as preference.

Question 2.
There are 20,000 members of a zoo. The percent of members having each membership type is shown in the circle graph. How many members have a contributor membership? What percentage of the noncontributory memberships are individual memberships? Round to the nearest percent. (Example 2)

Answer:
Total number of membership of zoo = 20,000
Percentage of contributor membership = 7.5%
Percentage of individual membership = 60%
Number member with contributor membership = \(\frac{7.5}{100}\) × 20,000
= 0.075 × 20,000
= 1500
Number member with individual membership = \(\frac{60}{100}\) × 20,000
= 0.6 × 20,000
= 12,000
Number of noncontributory membership = 20,000 – 1500 = 18,500
Percent of noncontributory who are individual = \(\frac{12000}{18500}\) × 100
= 0.6486 × 100
= 64.86%

Essential Question Check-In

Analyzing Categorical Data Worksheet Go Math 11.1 7th Grade Question 3.
When solving proportions based on data from graphs, why do you often convert from fractions and percents to decimals?
Answer:
When solving proportions based on data from graphs, we do often convert from fractions and percents to decimals because decimals are way to represent the fraction and percentage. When the fraction are calculated further we get decimal values and when it is multiplied by 100 we get the values in percentage (%)
Thus it helps in simplifying the calculation of problems.

Decimals helps in simplifying the calculation of problems.

Texas Go Math Grade 7 Lesson 11.1 Independent Practice Answer Key

The number of computers sold at an electronics store for each day of a week is shown in the dot plot.

Question 4.
What percent of all computers sold during the entire week were sold on Friday?
Answer:
The number of computers sold in each day in week:
Monday: 6
Tuesday: 9
Wednesday: 5
Thursday: 8
Friday: 12
Saturday: 7
Sunday: 3
Total of sold computers is 50.
Set up a proportion:

To find a percent of sold computers in friday, divide x by 100. Add a “%“ sign.
\(\frac{x}{100}\) = \(\frac{24}{100}\) = 0.24%
The percent of all computers sold in Friday is 0.24%

Question 5.
What percent of computers sold on weekdays were sold on Tuesday? Round to the nearest percent.
Answer:
Total of sold computers is 50.
The number of sold computers on Tuesday is 9.
Set up a proportion:

To find a percent of sold computers on Tuesday, divide x = 18 by 100 Add a “%“ Sign.
\(\frac{x}{100}\) = \(\frac{18}{100}\) = 0.18 ≈ 0.2%

A percent of sold computers on Tuesday is 0.2%.

Question 6.
Multiple Representations Suppose the data described above for the electronics store were represented with a bar graph instead of a dot plot. Would there be any advantages or disadvantages?
Answer:
Both bar graphs and dot plot have their own advantages and disadvantages depending on the person who uses it Both a bar graph and a dot plot are easier to interpret since the data are easily laid out However, for some,
they prefer a bar graph over a dot plot because in a bar graph, the actual numbers can be shown (the y-axis of the
graph) unlike in the dot plot where you just count the dots in order to determine the result.

Both bar graphs and dot plot have their own advantages and disadvantages depending on the person who uses it.

The number of states in the United States that are primarily in each of the time zones is shown in the bar graph.

Texas Go Math Grade 7 Answer Key Pdf Categorical Data Worksheet Question 7.
The continental United States is all states except Hawaii and Alaska. What percent of the continental states are primarily in the Eastern time zone?
Answer:
Calculate the percent of total continental states which are primarily in the Eastern time zone.

The percent of the continental states in the Eastern time zone is 43.68 %.

Question 8.
Is the percent of the continental states primarily in the Eastern time zone greater than or less than the percent of
all states that are in the Mountain or Central time zone?
Answer:
Calculate the percent of total continental states which are primarily in the Mountain and Central zone.

In percent of the continental states in the Eastern time zone is less than the percent of all continental states that are in the Mountain and Central time zone.

Question 9.
What If? Suppose the horizontal scale of the bar graph had intervals of 1 instead of 4. Would there be any advantages to having that scale? Would there be any disadvantages?
Answer:
The spread of the dot plots are:

• The data is almost equally distributed on both the side of centre which is “6”
• All the data is between 3 to 9
• Range of the given dot plot: 9 – 3 = 6

Range of given dot plot is 6

All of the boys attending a prom wore a tuxedo. The circle graph shows the number of boys wearing each of the different bow tie colors.

Question 10.
Make a Conjecture Estimate the percent of boys wearing black bow ties by comparing the black section of the graph to the whole graph.
Answer:
Calculate the percent of boys wearing black bow ties.
Boys wearing black bow ties 66 66

The percent of boys wearing black bow ties is 33 %.

Analyzing Data Worksheet Answer Key Lesson 11.1 Answer Key 7th Grade Question 11.
Calculate the percentage of boys wearing each bow tie color. How does the percentage of wearing black bow ties compare to your estimate?
Answer:
Calculate the percentage of boys wearing grey bow ties.

Calculate the percent of boys wearing white bow ties.

Calculate the percent of boys wearing blue bow ties.

Calculate the percent of boys wearing red bow ties.

Calculate the percent of boys wearing green bow ties.

Calculate the percent of boys wearing purple bow ties.

Grey bow ties: 12.5 %
White bow ties: 24 %
Blue bow ties: 11 %
Red bow ties: 9 %
Green bow ties: 65 %
Purple bow ties: 4 %
The percent of black bow ties is bigger than the percent of bow ties in others colors.

H.O.T. Focus on Higher Order Thinking

Question 12.
Communicate Mathematical Ideas A dot plot shows the number of pizzas sold at a local restaurant each day one week. One column of dots on the plot is much taller than the others. Explain what that means in the context of the data and of percents. Then describe how that same category would be noticeable on a circle graph of the same data.
Answer:
If one column of dots on the plot is much taller than the others column this means on that particular day of week
number of pizza sold at local restaurant is maximum as compared to the other days of week. So in a week the local restaurant sell heighest number of pizza on day that. Also in terms of percentage maximum percentage of pizza is sold on that day.

If same data is plotted on the circle graph than that particular day will have maximum area on the circle and the circle will be dividend in the number of days.

If one column of dots on the plot is much taller than the others column this means on that particular day of week number of pizza sold at local restaurant is maximum.

Question 13.
Analyze Relationships What is the relationship between the degree measure of the angle formed by the straight edges of a section of a circle graph and the percent of the data that the section represents?
Answer:
The relationship between the degree measure of the angle formed by the straight edges of a section of a circle
graph and the percentage of the data that the section represents are that both are directly proportional. If the
percentage of data is maximum then the angle formed in circle will be also maximum and if percentage of data is
minimum then the angle formed by circle will be also minimum.
Relation between angle of circle and percents of data is:
⇒ 100% = 360°
⇒ 1% = \(\frac{360^{\circ}}{100}\)
⇒ 1% = 3.6°

1% of data is equal to 3.6° on circle.

Question 14.
Multiple Representations A bar graph has 8 bars, all the same height. Suppose that a circle graph were used instead of a bar graph to represent the data. What percent ofthe data would each piece represent?
Answer:
It is given in the problem that there are 8 bars on bar graph and of equal height. So each bar will represent equal
percentage of the data. Hence in circle graph the circle will be divided in 8 equal parts and each single part will represent a bar of bar graph. We know that a complete circle is of 360°, so the single part of circle will \(\frac{360}{8}\) = 45°
Now finding each part of data (45°) in percentage:
360° = 100%
1° = \(\frac{100}{360} \%\)
So, 45° = \(\frac{100}{360}\) × 45%
= 12.50%
Hence, each piece wilt represent 12.50% of data.

Each piece will represent 12.50% of data.

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 12.1 Answer Key Populations and Samples.

Texas Go Math Grade 7 Lesson 12.1 Answer Key Populations and Samples

Texas Go Math Grade 7 Lesson 12.1 Explore Activity Answer Key  

Random and Non-Random Sampling

When information is being gathered about a group, the entire group of objects, individuals, or events is called the population. A sample is part of the population that is chosen to represent the entire group.

A vegetable garden has 36 tomato plants arranged in a 6-by-6 array. The gardener wants to know the average number of tomatoes on the plants. Each white cell in the table represents a plant. The number in the cell tells how many tomatoes are on that particular plant.

Because counting the number of tomatoes on all of the plants is too time-consuming, the gardener decides to choose plants at random to find the average number of tomatoes on them.

To simulate the random selection, roll two number cubes 10 times. Find the cell in the table identified by the first and second number cubes. Record the number in each randomly selected cell.

A. What is the average number of tomatoes on the 10 plants that were randomly selected?

B. Alternately, the gardener decides to choose the plants in the first row. What is the average number of tomatoes on these plants?

Reflect

Question 1.
How do the averages you got with each sampling method compare to the average for the entire population, which is 28.25?
Answer:
The averages obtained by both sampling methods are around the actual average of 28.5; the first method generated an average of 29.5 while the second method was 20.5.

Seventh Grade Answer Key Lesson 12.1 Texas Go Math Question 2.
Why might the first method give a closer average than the second method?
Answer:
The averages obtained by both sampling methods are around the actual average of 28.5; the first method generated an average of 29.5 while the second method generated 20.5. The first method’s average is closer to the actual average because it is more distributed and more random, unlike the second method.

The first method’s average is closer to the actual average because it is more distributed and more random, unlike the second method.

Reflect

Question 3.
You want to know the preferred practice day of all the players in a soccer league. How might you select a random sample?
Answer:
For example, you could survey one player from each soccer team.

Your Turn

Determine whether each sample is a random or biased sample. Explain your reasoning.

Question 4.
A librarian randomly chooses 100 books from the library’s database to calculate the average length of a library book.
Answer:
This is a random sample because each book, with different length, has an equal chance of being selected.

This is a random sample.

In Madison County, residents were surveyed about a new skateboard park. Determine whether each survey question may be biased. Explain.

A. Would you like to waste the taxpayers’ money to build a frivolous skateboard park?
This question is biased. It discourages residents from saying yes to a new skateboard park by implying it is a waste of money.

B. Do you favor a new skateboard park?
This question is not biased. It does not include an opinion on the skateboard park.

C. Studies have shown that having a safe place to go keeps kids out of trouble. Would you like to invest taxpayers’ money to build a skateboard park?
This question is biased. It leads people to say yes because it mentions having a safe place for kids to go and to stay out of trouble.

Your Turn

Determine whether each question may be biased. Explain.

Texas Go Math Grade 7 Lesson 12.1 Answer Key Question 5.
When it comes to pets, do you prefer cats?
Answer:
Yes, given question will be biased.
Because in given question name of the pet (cats) is already mentioned. So every pets will not have equal chance of being selected. And the answer for the asked question in the problem will be mostly in Yes or No.

Yes, given question will be biased

Question 6.
What is your favorite season?
Answer:
No, given question will not be biased.
Because in given question name of any season is not mentioned So every season will, have equal chance of being
selected. And the answer for the asked question in problem will the name of favourite season.

No, given question will not be biased.

Texas Go Math Grade 7 Lesson 12.1 Guided Practice Answer Key  

Question 1.
Follow each method described below to collect data to estimate the average shoe size of seventh grade boys. (Explore Activity)

Method 1

A. Randomly select 6 seventh grade boys and ask each his shoe size. Record your results in a table like the one shown.
Answer:

B. Find the mean of this data. Mean:
Answer:

Hence, the mean of shoe size of randomly selected student is 6.16

Method 2

A. Find the 6 boys in your math class with the largest shoes and ask their shoe size. Record your results in a table like the one shown in Method 1.
Answer:
Sample of six boys with largest shoes in my math class are:

B. Find the mean of this data. Mean: ____
Answer:

Hence, the mean shoe size of students is 8.33

Texas Go Math Grade 7 Populations and Samples Answer Key Question 2.
Method 1 produces results that are more/less representative of the entire student population because it is a random/biased sample. (Example 1)
Answer:
Method 1 produces results that are more representative of the entire student population because it is a random
sample.

Question 3.
Method 2 produces results that are more/less representative of the entire student population because it is a random/biased sample. (Example 1)
Answer:
Method 2 produces results that are less representative of the entire student population because it is a biased sample.

Question 4.
Heidi decides to use a random sample to determine her classmates’ favorite color. She asks, “Is green your favorite color?” Is Heidi’s question biased? If so, give an example of an unbiased question that would serve Heidi better. (Example 2)
Answer:
Yes, Heidi’s question is biased.
Because when Heidi is asking question she is particularly mentioning green colour so, here the sample (favourite colour of classmate) is not random. As soon as Heidi mention the green colour in her question the sample becomes the biased sample which means the outcome from her classmates will be in Yes or No.
Example of unbiased question that Heidi can ask from her classmate will be : Which is your favourite color?

Essential Question Check-In

Question 5.
Flow can you select a sample so that the information gained represents the entire population?
Answer:
When the sample are selected randomly from the entire groups or individual (which known as population) then the information gained represents the entire population.

Texas Go Math Grade 7 Lesson 12.1 Independent Practice Answer Key 

Question 6.
Paul and his friends average their test grades and find that the average is 95. The teacher announces that the average grade of all of her classes is 83. Why are the averages so different?
Answer:
The average of Paul and his friend (95) is different from the average announced by teacher (83) because when Paul is finding the average he is taking the biased sample. While finding the average Paul is considering only his and friends marks in test But in case of teacher while finding the average, teacher is taking random sample as teacher is considering the marks of each student in class while.

Paul is taking biased sample while teacher is taking random sample

Texas Go Math Book 7th Grade Answer Key Lesson 12.1 Question 7.
Nancy hears a report that the average price of gasoline is $2.82. She averages the’ prices of stations near her home. She finds the average price of gas to be $3.03. Why are the averages different?
Answer:
There is a difference in the average price of gasoline from the report ($2.82) and the gasoline price found by Nancy ($33.03) because when Nancy is finding the price she is considering the price of gasoline which is near to her home thus taking only biased sample in her calculation. But in case of price of report the calculation are done while taking the sample from everywhere which means the sample are taken randomly.

Nancy is taking biased sample but in case of report sample are taken randomly.

For 8-11, determine whether each sample is a random sample or a biased sample. Explain.

Question 8.
Carol wants to find out the favorite foods of students at her middle school. She asks the boys’ basketball team about their favorite foods.
Answer:
The sample will be biased sample
Because carol wants to know the favourite foods of students at middle school but she asks about it only with the basketball team out of whole middle school. So the population here is only the members of basketball team.

Question 9.
Dallas wants to know what elective subjects the students at his school like best. He surveys students who are leaving band class.
Answer:
The sample will be biased sample
Because Dallas wants to know the elective subjects of students which they liked best but she asks about it only with the students who are leaving band class. So the population here is only the students who are leaving the band class.

Question 10.
Karim wants to know what day of the week students at his school prefer. He randomly asks students each day in the cafeteria.
Answer:
The sample will be random sample
Because Karim wants to know the day of week which students prefer at his school and asks about it with the random students each day in cafeteria. So the population here is all the students of the school.

Question 11.
Members of a polling organization survey 700 registered voters by randomly choosing names from a list of all registered voters.
Answer:
The sample will be random sample
Because members of the potting organisation is surveying 700 registered voters by randomly and choosing the names from the list of registered voters. So the population here is all the 700 registered voters.

Determine whether each question may be biased. Explain.

Texas Go Math Grade 7 Pdf Population and Samples Answer Key Question 12.
Joey wants to find out what sport seventh-grade girls like most. He asks girls, “Is basketball your favorite sport?”
Answer:
Yes the question asked by Joey is biased.
Because joey while asking from seventh-grade girls that which sports do they Like, Joey mentions the name of basketball. So the population will be all the girls who like or not the basketball sports because they will reply in Yes or No. when this question will be asked the girls will not reply about their favourite sports.

Question 13.
Jae wants to find out what type of art her fellow students enjoy most. She asks her classmates, “What is your favorite type of art?”
Answer:
No, the question asked by Jae is not biased.
Because Jae has randomly asked from the fellow students about the art which enjoy the most So the population is all the fellow students of Jae.

Texas Go Math Grade 7 Lesson 12.1 H.O.T. Focus on Higher Order Thinking Answer Key 

Question 14.
Draw Conclusions Determine which sampling method will better represent the entire population. Justify your answer.

Answer:
The first sampling method in which Collin surveys 78 students randomly will better represent the entire population. The reasons for this are mentioned below :

• In case of Collin, surveys are being done on 78 students as compared to in the case of Karl where the survey is done only on 25 students. So larger number of samples will represent entire population the most.
• In case of Collin surveys sample are chosen randomly as compared to Karl’s survey where samples are chosen who are near hint during lunch.

Collin survey will better represent the entire population.

Practice and Homework Lesson 12.1 Answer Key 7th Grade Question 15.
Multistep Barbara surveyed students in her school by looking at an alphabetical list of 600 student names, dividing them into groups of 10, and randomly choosing one from each group.

a. How many students did she survey? What type of sample is this?
Answer:
Since there are 600 student names and they are divided into 10 groups, the number of students that were surveyed:
600 ÷ 10 = 60
Barbara surveyed 60 students
The sample done is called a random sample. A random sample is giving an equal chance of being selected.

b. Barbara found that 35 of the survey participants had pets. About what percent of the students she surveyed had pets? Is it safe to believe that about the same percent of students in the school have pets? Explain your thinking.
Answer:
The percent of the students that have pets from the 60 participants iS:
\(\frac{35}{60}\) × 100% ≈ 58%
The percentage of students having pets is somewhat reasonable as the basis for the same percentage of students in the school who have pets. This is because of the random sample and the result is a significant percentage of the students which is more than half of the surveyed participants.

Go Math Grade 7 Lesson 12.1 Answer Key Question 16.
Communicating Mathematical Ideas Carlo said a population can have more than one sample associated with it. Do you agree or disagree with his statement? Justify your answer.
Answer:
Basically, a population needs to have one sample. This sample is a part of the population that is chosen to represent the entire group (population). For some, they prefer random sampling, as this gives an equal chance of being selected from the population. However, there is also called a biased sample, in which the sample does not accurately represent the population. So the statement of Carlo really depends on how the sampling will take place and the survey question. For example, the population is a Math Club. The sample could be random or biased depending on the survey question and the manner of choosing the sample. For the question, it will be biased when you would ask, what is their favorite subject? It is very obvious that most of the sample will answer Math because the population is from the Math Club. It could be a random sample even when you randomly pick the participant and have a different question not related to being in a Math Club.

It depends on the survey question and population.

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 10.2 Answer Key Volume of Triangular Prisms and Pyramids.

Texas Go Math Grade 7 Lesson 10.2 Answer Key Volume of Triangular Prisms and Pyramids

Essential Question
How do you find the volume of a triangular prism or a triangular pyramid?

Finding the Volume of a Triangular Prism
The volume V of a prism is the area of its base B times its height h, or V = Bh .

Example 1
Find the volume of the triangular prism.
Step 1
Find the area of the triangular base.

Step 2
Find the volume of the triangular prism.

Reflect

Question 1.
What If? Suppose you know the volume V and base area B of a triangular prism. How could you find the height of the prism?
Answer:
raggedright The volume of a triangular prism is:
V = B . h (1)
We know the area of the base B and the volume of a triangular prism.
Divide (1) by B.

Your Turn

Lesson 10.2 Volume of a Triangular Prism Formula 7th Grade Question 2.
Find the volume of a garden seat in the shape of a triangular prism with a height of 30 inches and a base area of 72 in².
Answer:
V = B . h
We know the base B and the height of a prism.
B = 72 in²
h = 30 in
Substitute vaWe of base and height of a prism.
V = 72 . 30
= 2160 in³

The volume of a garden seat is 2160 in³.

Texas Go Math Grade 7 Lesson 10.2 Explore Activity Answer Key  

Exploring the Volume of a Triangular Pyramid

Previously you explored the volumes of rectangular prisms and pyramids. Now you will repeat the same activity with triangular pyramids and prisms that have the same height and congruent bases.

Step 1
Make three-dimensional models. Make larger versions of the nets shown. Make sure the bases and heights in each net are the same size. Fold each net, and tape it together to form an open prism or pyramid.

Step 2
Fill the pyramid with bears. Make sure that the beans are level with the opening of the pyramid. How many pyramids full of beans do you think
it will take to fill the prism? ________________________
Pour the beans into the prism. Repeat until the prism is full.
Was your conjecture supported?

Step 3
Write a fraction that compares the volume of the pyramid to the volume of the prism.

Reflect

Question 3.
Analyze Relationships Does it appear that the relationship between the volume of triangular pyramids and prisms is the same as that for rectangular pyramids and prisms?
Answer:
The volume of the triangular pyramids and prisms with congruent bases and heights is the same as how the
volume of rectangular pyramids and prisms are determined. The relationship between the two is the same in
which the volume of the triangular pyramid is \(\frac{1}{3}\) the volume of the triangular prism.

Yes

Lesson 10.2 Answer Key Volume of Prisms and Cylinders Answers Question 4.
Draw Conclusions Write a formula for the volume of a triangular pyramid with a base area of B and a height of h.
Answer:
We know that the volume V of a triangular pyramid is the area of its base B times its one-third of height h.
Formula for volume = \(\frac{1}{3}\)Bh
where, B is area of base and h is height of triangular pyramid.

V = \(\frac{1}{3}\)Bh

Your Turn

Question 5.
The volume of a triangular pyramid is 13.5 m³. What is the volume of a triangular prism with a congruent base and the same height? Explain.
Answer:
ragged right The volume of a triangular prism is
V = B . h (1)
The volume of triangular pyramid is
V_P = \(\frac{1}{3}\)B . h (2)
They have same value for base and height.
Multiply (2) by 3
3V_P = B . h = V
The volume of a triangular prism is three time as big as the volume of a pyramid.
The volume of a triangular prism is:
V = 3 . V_P = 3 . (13.5) = 40.5 m³
The volume of a triangular prism is three time as big as the volume of a pyramid.
The volume of a triangular prism is:
V = 3 V_P = 40.5 m³

Example 2
Mr. Martinez is building wooden shapes for a sculpture in the park. His plans show a triangular pyramid and a triangular prism, and each shape is 5 feet high. The base of each shape is a triangle with a base of 2.5 feet and a height of 2 feet. How much greater than the volume of the pyramid is the volume of the prism?

Step 1
The triangular base is the same for both shapes. Find the area of the base B.

The area of the base B for both shapes is 2.5 ft².

Step 2
Find the volume of the prism.
V = Bh Use the formula.
V = (2.5) × 5 = 12.5 Substitute the value for B and h of the prism.
The volume of the prism is 12.5 ft³.

Step 3
Find the volume of the pyramid.
Volume of pyramid = \(\frac{1}{3}\) . volume of prism
= \(\frac{1}{3}\) . 12.5 ≈ 4.2 Substitute and calculate.
The volume of the pyramid is approximately 4.2 ft³.

Step 4
Compare the volumes.
Volume of prism – volume of pyramid = 12.5 – 4.2 = 8.3
The volume of the prism is 8.3 ft³ greater than that of the pyramid.

Your Turn

Go Math Grade 7 Lesson 10.2 Answer Key Question 6.
How much greater is the volume of a triangular prism with a base area of 14 cm² and a height of 4.8 cm than the volume of a triangular pyramid with the same height and base area?
Answer:
Use the formula for a prism.
V = B . h
B = 14 cm² Base area of a prism
h = 4.8 cm Height of a prism
y = 14 . (4.8)
V = 67.2 cm³ The volume of a prism
Use formula for a pyramid.
V = \(\frac{1}{3}\) . B . h = \(\frac{1}{3}\) . volume of a prism
= \(\frac{1}{3}\) . (67.2)
V = 22.4
Volume of a prism – volume of a pyramid = 44.8 cm³
The volume of a prism is 44.8 cm³ greater than that of the pyramid.

Texas Go Math Grade 7 Lesson 10.2 Guided Practice Answer Key  

Question 1.
Find the volume of the triangular prism. (Example 1)

Find the area of the base of the prism.
Use the equation A = ______ bh.
A = ___ (___) (___) = ___ in²
Find the volume of the prism. Use the equation V = Bh.
V = (___)(___) = ___ in³
Answer:
b = 3 in Length of base
h = 3 in Height of base
h = 16 in Height of a prism
A = \(\frac{1}{2}\) . b. h
A = \(\frac{1}{2}\) . 3 . 3 = \(\frac{9}{2}\) = 4.5 in²
V = B . h
V = (4.5) . 16 = 72 in³
V = 72 in³

Question 2.
A triangular pyramid and a triangular prism have congruent bases and the same height. The triangular pyramid has a volume of 90 m³. Find the volume of the prism. (Explore Activity)
The volume of the prism is ___ because the volume of the prism is ___ times the volume of the pyramid.
Answer:
The volume of a prism is:
V = B . h
The volume of a pyramid is:
V_P = \(\frac{1}{3}\) . B . h
They have congruent bases and the same height so the volume of the prism is:

The volume of the prism is
270 m³
because the volume of the prism is three times the volume of the pyramid.

Texas Go Math Grade 7 Volume Triangular Prism Answer Key Question 3.
In Exercise 2, how much greater is the volume of the prism than the volume of the pyramid? (Example 2)
Answer:
The volume of the pyramid is only of the volume of the prism. Since the volume of the prism is 270 m³ and the volume of the pyramid is 90 m³. The volume of the prism is greater than the volume of the pyramid by 180 m³

Find the volume of each figure.

Question 4.

Answer:
b = 9 ft Lenghtofthe base
H = 5 ft Height of a prism
h = 9 ft Height of the base
Find the area of the base B We have triangular base, so we use the formula:
B = \(\frac{1}{2}\) . b . h = \(\frac{1}{2}\) . 9 . 9 = \(\frac{81}{2}\) = 40.5 ft²
Use the formula for the voLume of a prism.
V = B . H= (40.5) . 5 = 202.5 ft³

V = 202.5 ft³

Question 5.

Answer:
l = 6ft Lenght of the base
w = 6 ft Width of the base
h = 6 ft Height of a pyramid
Find the area of the base B.
B = l . w = 6 . 6 = 36 ft²
Use tne formula.
V = \(\frac{1}{3}\) . B . h

V = 72 ft³

Question 6.

Answer:
a = 7 in The leg of a right triangle
b = 10 in The leg of a right triangle
h = 5 in Height of a prism
Find the area of the base B.

Use the formula.
V = B . h = 35.5 = 175 in³

V = 175 in³

Essential Question Check-In

Lesson 10.2 Volume of Prisms and Cylinders Answer Key Question 7.
A pyramid has a base that is a triangle. The length of the base of the triangle is 5 meters, and the height of the triangle is 12 meters. The height of the pyramid is 10 meters. How would you explain to a friend how to find the volume of the pyramid?
Answer:
b = 5 m Length of base
h_B = 12 m Height of base
h = 16 m Height of a pyramid
Find the area of the base B. The base is in the shape of a triangle. Use the formula:

Use the formula for the volume of a triangular pyramid:

The volume of the triangular pyramid is 160 m³.

Texas Go Math Grade 7 Lesson 10.2 Independent Practice Answer Key  

Question 8.
A trap for insects is in the shape of a triangular prism. The area of the base is 3.5 in2 and the height of the prism is 5 in. What is the volume of this trap?
Answer:
A trap for insect is in the shape of triangular prism, so use the formula for the volume of a triangular prism.
B = 3.5 in² Base of a prism
h = 5 in Height of a prism
The volume of a prism is
V = Bh = (3.5) . 5 = 17.5 in³
The volume of a trap for insect is 17.5 in³.

Question 9.
Arletta built a, cardboard ramp for her little brothers’ toy cars. Identify the shape of the ramp. Then find its volume.

Answer:
A cardboard ramp is in the shape of a triangular prism. Use the formula for the volume of a triangular prism.
a = 25 in Length of one side of the triangle
b = 6 in Length of other side of the triangle
h = 7 in Height of a prism
Find the area of the base B.

The volume of a triangular prism is:
V = B . h = 75 . 5 = 525 in³

The volume of a cardboard ramp is 525 in³.

Go Math Chapter 10 Lesson 10.2 Answer Key Question 10.
Represent Real-World Problems Sandy builds this shape of four congruent triangles using clay and toothpicks. The area of each triangle is 17.6 cm², and the height of the shape is 5.2 cm. What three-dimensional figure does the shape Sandy built resemble? If this were a solid shape, what would be its volume? Round your answer to the nearest teñth.

Answer:
Sandy built a three-dimensional figure which resemble on the triangular pyramid
B = 17.6 cm² Base of pyramid
h = 5.2 cm Height of a pyramid
Use the formula for the volume of a pyramid.
V = \(\frac{1}{3}\) . 17.6 . 5.2
= 30.50 ≈ 31 cm³

Sandy built a three-dimensional figure which resemble on the triangular pyramid.
The volume of the triangular pyramid is 31 cm³.

Question 11.
Draw Conclusions Would tripling the height of a triangular prism triple its volume? Explain.
Answer:
B = B Base area
h = h Height of a prism
Use the formula for the volume of a triangular prism.
V₁ = Bh
Now triple the height of a prism.
B = B Base area
h = 3 . h Height of a prism
Use the formula for the volume of a triangular prism.
V₂ = B . 3 . h = 3 (B . h) = 3 . V₁

The tripling height of a triangular prism triples its volume.

Go Math Grade 7 Chapter 10 Lesson 10.2 Answer Key Question 12.
The Jacksons went camping in a state park. One of the tents they took is shown. What is the volume of the tent?

Answer:
b = 4.5 ft Length of base
h_B = 3.5 ft Height of base
h = 6ft Height of a prism
Find the area of the base B. The tent is in the shape of a triangular prism. A prism has a base that is a triangle, so use the formula:
B = \(\frac{1}{2}\) . b . h_B = \(\frac{1}{2}\)(4.5) . (3.5) = 7.875 ft²
The volume of a triangular prism is:
V = B . h = (7.875) . 6 = 47.25 ft³
The volume of the tent is 47.25 ft³.

Question 13.
Shawntelle is solving a problem involving a triangular pyramid. You hear her say that bee” is equal to 24 inches. How can you tell if she is talking about the base area B of the pyramid or about the base b of the triangle?
Answer:
Shawntelle while solving a problem she say ‘bee’ is equal to 24 inches. So she is definitely talking about the base
b of the triangle not the base area B. Because she use the unit of base as inches not inch². If she was taking about the base area then she would have must mentioned the unit as inch² inches of inches.
Hence, she is talking about the base b of the triangle not base area B.

Question 14.
Alex made a sketch for a homemade soccer goal he plans to build. The goal will be in the shape of a triangular prism. The legs of the right triangles at the sides of his goal measure 4 ft and 8 ft, and the opening along the front is 24 ft. How much space is contained within this goal?

Answer:
b = 4 ft Length of base
h_B = 8 ft Height of base
h = 24 ft Height of a prism
Find the area of the base B. The base is in the shape of triangle. Use the formula:

Use the formula for the volume of a triangular prism.
V = B . h = 16 . 24 = 384 ft³
This goal contained 384 ft³ of space.

Texas Go Math Grade 7 Lesson 10.2 Higher Order Thinking Answer Key  

Question 15.
A plastic puzzle in the shape of a triangular prism has bases that are equilateral triangles with side lengths of 4 inches and a height of 3.5 inches. The height of the prism is 5 inches. Find the volume of the prism.
Answer:
b = 4 in Length of base
h_B = 3.5 in Height of base
h = 5 in Height of a prism
Find the area of the base B. The base is in the shape of a triangle. Use the formula:

Use the formula for the volume of a triangular prism.
V = B . h
= 7 . 5
= 35 in³

The volume of the prism is V = 35 in³.

Go Math 7th Grade Lesson 10.2 Homework Answer Key Question 16.
Persevere in Problem-Solving Lynette’s grandmother has a metal doorstop with the dimensions shown. Find the volume of the metal in the doorstop. The metal in the doorstop has a mass of about 8.6 grams per cubic centimeter. Find the mass of the doorstop.

Answer:
b = 10 cm Length of base
h_B= 6 cm Height of base
h = 2.5 cm Height of a prism
Find the area of the base B. The base in the shape of triangle. Use the formula:

Use the formula for the volume of a triangular prism.
V = B . h = 30 . (2.5) = 75 cm³
Mass of the doorstep is 75 . (8.6) = 645\(\frac{\mathrm{g}}{\mathrm{cm}^{3}}\).

The volume of the metal in the door step is V = 75 cm³.
Mass of the doorstep is 645\(\frac{\mathrm{g}}{\mathrm{cm}^{3}}\).

Question 17.
Make a Conjecture Don and Kayla each draw a triangular pyramid that has a volume of 100 cm³. They do not draw identical shapes. Give a set of possible dimensions for each pyramid.
Answer:
Since Don and Kayta did not draw identical shapes of a triangular pyramid. The possible dimensions for the
triangular pyramid with volume of 100 cm³ are:

• base = 15 cm; height = 10 cm; Height = 4 cm
• base = 10 cm; height = 12 cm; Height = 5 cm
• base = 12 cm; height = 5 cm; Height = 10 cm
• base = 5 cm; height = 10 cm; Height = 12 cm

The possible dimensions for the triangular pyramid with volume of 100 cm³.

Question 18.
Multistep Don’s favorite cheese snack comes in a box of six pieces. Each piece of cheese has the shape of a triangular prism that is 2 cm high. The triangular base of the prism has a height of 5 cm and a base of 4 cm. Find the volume of cheese in the box.

Answer:
Each piece of cheese has the shape of a triangular prism.
For one piece the volume is:
b = 4 cm Length of base
h_B = 5 cm Height of base
h = 2 cm Height of a prism
Find the area of the base B.

Use the formula for the volume of a triangular prism.
V_c = B . h = 10 . 2 = 20 cm³
We have six pieces in the box, so the volume of cheese in the box is:
V = 6 . V_c = 6 . 20 = 120 cm³

The volume of cheese in the box is V= 120 cm³.

Go Math Grade 7 Answer Key Pdf Volume of Triangular Prism Answer Key Question 19.
Analyze Relationships What effect would doubling all the dimensions of a triangular pyramid have on the volume of the pyramid? Explain your reasoning.
Answer:
B = B Base area
h = h Height of a pyramid
Use the formula for the volume of a triangular pyramid.
V₁ = \(\frac{1}{3}\) . B . h
Now double all the dimensions of the triangular pyramid.
B = 2 . B Base area
h = 2 . h Height of a pyramid
Use the formula for the volume of a triangular pyramid.
V₂ = \(\frac{1}{3}\) . 2 . B . 2 . h
= \(\frac{1}{3}\) . 4 . (B . h)
= 4 . \(\frac{1}{3}\) . (B . h)
= 4 . V₁
Doubting at the dimension of a triangular pyramid, its volume is quadrupling

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 13.3 Answer Key Making Purchasing Decisions.

Texas Go Math Grade 7 Lesson 13.3 Answer Key Making Purchasing Decisions

Example 1.
Silvie went to a local warehouse store to buy her family’s favorite sports drink. Which of the two options described below is the better buy?

Step 1
Find the total amount of the sports drink in each purchase.
Value Pack: 24(0.5) = 12 liters
Sport pack: 18(0.75) = 13.5 liters
Step 2
Find each unit price.

The Value Pack is a better buy, because $0.77 < $0.88.

Your Turn

Grade 7 Go Math Answer Key Lesson 13.3 Answer Key Question 1.
Financial Literacy Manny must choose between a pack of four 6.5-ounce containers of yogurt for $3.77 or three 8-ounce containers at $1.29 each. Which ¡s the better buy? Why?
Answer:
Find the total. amount of the yogurt in each purchase.
A pack of 46.5 – ounce containers
4 × 6.5 = 26 – ounces
A pack of 38- ounce containers
3 × 8 = 24 – ounces

Now, find each unit price.
A pack of 46.5-ounce containers
\(\frac{\$ 3.77}{26-\text { ounces }}\) = $0.145 per ounce

A pack of 38-ounce containers
Each 8—ounce container costs $1.29. hence the price of 3 containers is
3 × $1.29 = $3.87.
\(\frac{\$ 3.87}{24-\text { ounces }}\) = $0.16 per ounce

Better buy is a pack of 4 6.5— ounce containers, because $0.145 < $0.16

Example 2
Nathan plans on hiking this summer and wants to buy a solar charger for his cell phone and notebook computer. He finds the charger that he wants at two stores. Which store has the lower price for the charger?


Answer:
Step 1
Find the discount price at each store.
Kitt’s
discount price = regular price – discount
= $89.99 – 0.3($89.99)
= $89.99 – $26,997
= $62,993
To the nearest cent, the discount price at Kitti’s is $62.99

Rec Plus
discount price = regular price – discount
= $79.99 – $15.00
= $64.99
The discount price at Rec Plus is $64.99.

Step 2
Compare the discounted prices.
Kitt’s offers the lower price, because $62.99 < $64.99.

Reflect

Question 2.
Critical Thinking Why might Nathan choose the higher priced item?
Answer:
Nathan would choose the charger in Kitt’s even if it has a higher regular price. This is because the discount in Kitt’s is higher compared to the Rec Plus. Once the regular price for the charger in Kitt’s got discounted, the price is cheaper compared to the discounted price in Rec Plus.

The discount is higher for the higher-priced item which made it cheaper after the discount

Your Turn

Go Math Lesson 13.3 Answer Key Grade 7 Question 3.
Nathan finds a backpack at Kitt’s that is regularly $84.99 but is on sale for \(\frac{1}{3}\) off. The same backpack is regularly $72.99 at Rec Plus but is on sale for 25% off. Which is a better buy? Explain.
Answer:
Find the discount price at each store.
Kitts
Discount price = Regular price – Discount
To find the Discount, multiply the Regular price by the percent of the discount.
$84.99 × \(\frac{1}{3}\) = $28.33
Discouut price = $84.99 – $28.33
Discount price = $56.66
The Discount price at Kitt’s is $56.66.
Rec Plus
Discount price = Regular price – Discount
To find the Discount multiply the Regular price by the percent of discount. Write the percent as decimal, ie 25% = 0.25.
$72.99 × 0.25 = $18.25
Discount price = $72.99 – $18.25
Discount price = $54.74
Tue Discount price at Rec Plus is $54.74.
Rec Plus offers the lower price, because $54.74 <$56.66.

Example 3.
Cedelia can get the same running Go shoes at two different stores. She wants to get two pairs of the same style. Which is the better buy?

Go Run

She pays $104 for 2 pairs.
Shoe Shoppe

She pays 2 × $59 = $118 for 2 pairs
Go Run has the better buy because $104 < $118.
Answer:

Reflect

Question 4.
What If? Suppose the total price at Shoe Shoppe had been $103? What are some conditions of a rebate that would make it a better decision to buy the shoes at Go Run?
Answer:
First condition
If the first pair has rebate at least $7 and you get second pair free.
Proof:
Regular price is $109, rebate is at least $7, hence the total price at Go Run is $109 — $7 = $102.
$102 < $103
Hence, Go Run lias the better buy than Shoe Shoppe.

Second condition
If both pairs have a discount of 53%.
Proof:
The regular price is $109.
Discount price = Regular price – Discount
To find the Discount multiply the Regular price by the percent of discount.
Write percent as decimal, ie 53% = 0.53.
$109 × 0.53 = $57.77

Discount price = $109 – $57.77
Discount price = $51.23
The Discount price of one pair is $51.23, and the discount price of 2 pairs is
$51.23 × 2 = $102.16
$102.46 < $103
Hence, Go Run is a better buy than Shoe Shoppe.

First condition: If the first pair has a rebate at least $7 and you get the second pair free.
Second condition: If both pairs have a discount of 53%.

Your Turn

Go Math Answer Key Grade 7 Lesson 13.3 Question 5.
Greta wants to buy 3 jars of honey. Food Mart sells it for $8.99 with a “Buy 2, get 1 free” offer. Leona’s sells it for $8.49 with a coupon for 50% off with a limit of 2 coupons. Which store has the better deal?
Answer:
Food Mart
Greta wants to buy 3 jars of honey, and Food Mart has an offer if you buy 2 you get 1 free.
Hence, Greta will buy 2 jars of honey and get one free, and that would be 3 jars of honey she needs.
One jar costs $8.99. so
Price of 2 jars = 2 × $8.99 = $17.98
Greta would pay $17.98 for 3 jars of honey at Food Mart.

Leona‘s
At Leon’s she can buy 2 jars with a coupon for 50% off, because there is a limit of 2 coupons.
Hence, the third jar of honey she has to buy by the full price.
One jar of honey costs $8.19.
Let’s find the Discount price with a coupon.
Discount price = Regular price – Discount
To find the Discount multiply the Regular price by the percent of discount.
Write percent as decimal, ie 50% = 0.5.
$8.19 × 0.5 = $4.215
Discount price = $8.49 – $4.245
Discount price = $4.245

The Discount price of one jar of honey is $4.245.
She would buy 2 jars of honey by the discount price and the third one by the full price.
Hence
Price of 3 jars = 2 × Discount price + Full price
Price of 3 jars = 2 × $4.245 + $8.49
Price of 3 jars = $16.98
Greta would pay $16.98 for 3 jars of honey at Leona’s.
Hence, Leon’s has the better buy, because $16.98 < $17.98.

Texas Go Math Grade 7 Lesson 13.3 Guided Practice Answer Key  

Which is the better buy? Write an inequality to justify your answer.

Question 1.
The Corner Store sells 4 bottles of energy drink for $1 1.56. Bev’s sells 6 bottles for $17.94. Which is the better buy? (Example 1)

Answer:
Find the price of one energy drink in each purchase.
The Corner Store
4 bottles of energy drink cost $11.56.
Find the price of one bottle of energy drink.
Price of one bottle = \(\frac{\$ 11.56}{4}\) = $2.89/bottle
The price of one bottle at Coriier Store is $2.89 per bottle.

Bev’s
6 bottles of energy drink cost $17.94.
Find the price of one bottle of energy drink.
Price of 0ne bottle = \(\frac{\$ 17.94}{6}\) = $2.99/bottle
The price of one bottle at Bev’s is $2.99 per bottle.
The Corner Store lias the better buy, because $2.89 < $2.99.

The Corner Store has the better buy, because $2.89 <$2.99.

Lesson 13.3 Independent Practice Answer Key Question 2.
You can buy a 2-pound loaf of bread for $2.50 or a 2-pack of 1\(\frac{1}{2}\)-pound loaves for $3.30. Which is the better buy?(Example 1)
Answer:
Find the price of 0ne pound loaf of bread in each purchase.
First purchase
2-pound loaf of bread for 82.50
Find the price of one pound loaf of bread.
Price of one pound = \(\frac{\$ 2.50}{2}\) = $1.25
The price of one pound of loaf of bread is $1.25.
Second purchase
2- pack of 1\(\frac{1}{2}\)– pound loaf of bread for $3.30
In this purchase we have 2-pack of 4\(\frac{1}{2}\) = \(\frac{3}{2}\) = 1.5- pound loaves.
Hence, the whole purchase will be 2 × 1.5 =3.
So, 3- pound loaf of bread costs $3.30.
Find the price of one pound loaf of bread.
Price of one pound = \(\frac{\$ 3.30}{3}\) = $1.1
The price of one pound of loaf of bread is $1.1.
Second puchase is the better, because $1.1 < $1.25.

Question 3.
Marta can buy a 6-pack of 15-ounce cans of broth for $11.29 or three 32-ounce containers for $10.97. Which is the better buy? (Example 1)

Answer:
First purchase
A 6- pack of 15- ounce cans of broth
6(15) = 90 oz
Now, find unite price
\(\frac{\$ 11.29}{90-\mathrm{oz}}\) = $0.125/oz

Second purchase

A 3-32- contains
3(32) = 96 oz
Now, find unite price
\(\frac{\$ 10.97}{96-\text { ounces }}\) = $0.11/oz
Second purchase is the better, because $0.11 <$0.125.

Question 4.
Zena can get an item online for $19 that weighs 8 pounds. Shipping and handling costs $0.49 per pound. She can also buy the same item locally for $26.95, and she has a $5 off coupon. Which is the better buy? (Example 2)
Answer:
The item has 8 pounds and shipping and handling per pound is $0.49.
Shipping and handling for item is
$0.49 × 8 = $3.92
To find the whole price of item sum the online price and the cost of shipping and handling.
$19 + $3.92 = $22.92
Online purchase costs $22.92.

Locally purchase
$5 off coupon is a Discount.
Find the Discount price.
Discount price = Regular price — Discount
Discount price = $26.95 — $5
Discount price = $21.95
The Discount price for locally purchase is $21.95.
The locally purchase is better, because $21.95 <$22.92.

Question 5.
A take-and-bake pizza chain has several coupons, which cannot be used together. J.D. is buying a pizza that costs $17.90. Should he use a $5 off coupon or a 35% off coupon? (Example 2)
Answer:
$5 off coupon
$5 off coupon is a Discount.
Find the Discount price.
Discount price = Regular price – Discount
Discount price = $17.90 – $5
Discount price = $12.90
The Discount price of a pizza with a $5 off coupon is $12.90.

35% off coupon
Discount price = Regular price – Discount
To find the Discount multiply the Regular price by the percent of discount.
Write percent as decimal, ie 35% = 0.35.
$17.90 × 0.35 = $6.26
Discount price = $17.90 – $6.26
Discount price = $11.64
The Discount price of a pizza with a 35% coupon off is $11.64.
J.D. should use a 35% off coupon, because $11.61 <$12.90.

Question 6.
The King family buys an HDTV selling for $825 at PanView with a 20% off coupon and a rebate of $125. They later see the TV on sale at Rey’s TVs for $555. Did they get the better deal? (Example 3)
Answer:
Determine the cost of the HDTV the King fami[y purchased at PanView. Show the 20% off coupon as decimaL
825 × 0.20 = 165 Determine the discount for the HDTV
825 – 165 = 660 Subtract the discount from the original price
660 – 125 = 535 Subtract the rebate from the discounted price
The King family get the better deal. purchasing the HDTV at PanView instead at Rey’s TVs
Yes

Question 7.
Credit card A has an annual fee of $50 but gives you a rebate at the end of the year of 2% of your total purchases. Credit card B has no annual fee or rebate. If you spend about $150 a month, which card is better for you? (Example 3)
Answer:
Credit card A
If you spend $150 a month, it means that you spend 12 × $150 = $1,800 a year.
Credit card A has an annual fee of $50, hence, we have to add fee to the amount you spend a year.
$1,800 + $50 = $1,850
At the end of the year you get a rebate of 2% of your total purchase, hence we have to subtract 2% from the whole amount $1,850.
Write percent as decimal, ie 2% = 0.02.
Find 2% of $1,850.
$1,850 × 0.02 = $37
Now subtract.
$1,850 – $37 = $1,813
If you use Credit card A, you will spend $1,813 a year.

Credit card B
Credit card B has no annual or rebate, hence, yearly you will spend
12 × $150 = $1,800
If you use Credit card B, you will spend $1,800 a year.

Hence, the Credit card B is better, because $1,800 < $1,813.

Essential Question Check-In

Question 8.
Is the lower unit price always the best buy?
Answer:
No, it is not always.
Sometimes there is an offer like, “Buy 2, get 1 free” of items with higher unit price.
Also, there is some discount on quantity on items with higher unit price, which could be better buy than buy of unit with lower unit price without discount.
The quality of the product when you buy it, regardless of the price, should not be neglected.

Texas Go Math Grade 7 Lesson 13.3 Independence Practice Answer Key   

Question 9.
Store 1 has a price of $99 on an MP3 player. Store 2 is offering the same MP3 player at a sale price of 25% off their regular price of $125. Jerusha wants to buy an MP3 player. From which store should she buy it? Explain.
Answer:
Store 2
Discount price = Regular price – Discount
To find the Discount multiply the Regular price by the percent of discount.
Write percent as decimal, ie 25% = 0.25.
Discount = $125 × 0.25 = $31.25
Discount price $125 – $31.25
Discount price = $93.75
The Discount price of an MP3 player in Store 2 is $93.75.

The price of an MP3 player in Store 1 is $99.
He should buy an MP3 player in Store 2, because $93.75 < $99.

Question 10.
Multistep Randy wants trail mix for his hiking trip. The ready-made trail mix costs $8.95 for 1.5 pounds. The costs of the bulk ingredients to make one pound of trail mix are as follows: salted peanuts—$1.25, raisins—$1.70, sunflower seeds—$0.50, cashews—$0.87, and almonds—$0.65. If Randy plans to take 6 pounds of trail mix, which option is cheaper? How much does he save by choosing the cheaper option?
Answer:
The ready-made trail mix
A pack of 1.5 pounds costs $8.95. and Randy wants to buy 6 pounds of it.
Hence, he needs to buy 1 packs of 1.5 pounds of trail mix.
The cost of 6 pounds of ready—made trail mix will be
4 × $8.95 = $35.8
6 pounds of ready-made trail mix will cost $35.8.
Self—made trail mix
To find the cost of one pound of trail mix. prices of all ingredients should be summed up.
One pound of self-made trail mix = $1.25 + $1.70 + $0.50 + $0.87 + $0.65 = $4.97
To find the cost of 6 pounds of self-made trail mix multiply by 6 the cost of one pound.
6 × $4.97 = $29.82
The cost of 6 pounds of self-made trail mix will be $29.82.

The self-made trail mix is cheaper option than the readymade trail mix, because $29.82 < $35.8.

Grade 7 Go Math Practice and Homework Lesson 13.3 Answer Key Question 11.
Tyron and Penelope both bought 4-wheelers. Tyron paid $199 upfront and will pay the remainder in 12 payments of $50 each. Penelope paid nothing up front, and will make 18 payments of $49. Who got the better buy? Explain.
Answer:
Tyron
To find how much Tyron paid 4—wheeler, sum the amount he paid up front and the total remainder.
First, find the total remainder.
To find the total remainder multiply the number of payments by the amount of each payment.
The total remainder = 12 × $50 = $600
Now, find the total cost.
The total cost of 4—wheeler = $199 + $600 = $799
Tyron paid $799 for 4—wheeler.

PeneloPe
Unlike Tyron Penelope will pay the price in 18 payments of $49.
To find the total cost multiply the number of payments by the amount of each palyment.
The total cost of 4—wheeler = 18 × $19 = $882
Penelope paid $882 for 4—wheeler.
Tyron lias the better buy that Penelope, because $799 < $882.

Question 12.
Financial Literacy T’Shonda is buying a laptop computer. She will pay 8% sales tax on the price before ány rebates. Where will she get a better buy? Explain.

Answer:
XYZ-Tronic
First, find the sales tax on the price(Subtotal).
Write the tax rate as decimal, ie 8% = 0.08
Tax = Subtotal × Tax rate
Tax = $629 × 0.08 = $50.32
Now, add the subtotal and the tax to find the total price.
Total price = $629 + $50.32 = $679.32
The Total price before rebate is $679.32
To find the price after rebate, subtract mail—in—rebate from the Total price.
The price after rebate = $679.32 – $150 = $529.32
In XYZ-Tronic she would pay $529.32 for a laptop.

Tec U—Comp
First, find the sales tax on the price(Subtotal).
Write the tax rate as decimal. ie 8% = 0.08
Tax = Subtotal × Tax rate
Tax = $649 × 0.08 = $51.92
Now, add the subtotal and the tax to find the total price.
Total price = $649 + $51.92 = $700.92
The total price before rebate is $700.92

To find the price after rebate(The Discount price), subtract the Discount of 25% from the Total price(Regular price).
Discount price = Regular price — Discount
To find the Discount multiply the Regular price by the percent of discount.
Write percent as decimal, ie 25% = 0.25.
Discount = $700.92 × 0.25 = $175.23
Discount price = $700.92 – $175.23
Discount price = $525.69
The Discount price of a laptop is $525.69.
T’Shonda will get the better buy in Tec—U-Comp, because $525.69 < $529.32.

Question 13.
Critical Thinking What single discount is equal to a discount of \(\frac{1}{4}\) off followed by an additional 10% off the sale price?
Answer:
We want to know what single discount is equal to these discounts together.
First, there is a discount of 25%.

Write a fraction as decimal, ie \(\frac{1}{4}\) = 0.25
Now, write the decimal as percent, ie 0.25 = 25%
Hence, when some item has discount of \(\frac{1}{4}\), it means that item has discount of 25%.
After the discount of 25%, the total cost of that item is actually 75% of the regular price(the regular price
represents 100% of the item) of that item, because 100% – 25% = 75%.

After the discount of 25%, there is an additional. discount of 10%.
An additional discount of 10% we can not compute on 100% of item price, because now the actual cost of the
item is 75% of the first regular price(because first we had a discount of 25%).
So, now we have to find 10% of 75% and subtract from it
Write percent as decimal, ie 10% = 0.1
To find 10% of 75%, multiply 75% by the percent written in decimal.
75% × 0.1 = 7.5%
Now, subtract.
75% – 7.5% = 67.5%

Finally, the total cost of the item with first discount of 25% and then an additional 10% is 67.5% of the reguLar
price of that item.
As the cost of an item is now 67.5%, this means that these two discounts together represent a 32.5% discount,
because 100% – 67.5% = 32.5%.
Hence, the single discount that is equal to a discount of \(\frac{1}{4}\) off followed by an additional 10% off is 32.5% off.

The single discount that is equal to a discount of \(\frac{1}{4}\) off followed by an additional 10% off is 32.5% off.

Question 14.
Make a Conjecture John is comparing the prices of two bags of the same cereal. He notices that the larger bag holds 10 more ounces and costs $1.50 more. How can he use the unit price of the smaller bag to decide the better buy? Explain.
Answer:
John can use the unit price of the smaller bag by multiplying it by 10 since the larger bag contains 10 more ounces. If the result of this is more than $1.50, then it is better to buy the larger bag instead of the smaller bag. But if the result is less than $1.50, it is still better to buy the smaller bag.

Multiply the unit price of the smaller bag by 10.

Texas Go Math Grade 7 Lesson 13.3 H.O.T. Focus on Higher Order Thinking Answer Key   

Question 15.
Draw Conclusions Mr. Jaros has the following options for buying a digital video recorder and access to the recording service for 2 years.
DiV: $49.99 digital video recorder, 2-year subscription at $16.98 a month
TVU: Free digital video recorder, 2-year commitment at $19.95 a month
a. Which is the better deal? Explain.
Answer:
DiV
To find the total cost. of a digital video recorder and access to the recording service for 2 years we have to sum the cost of digital video recorder and the total cost of 2—year subscription.
To find the total cost of subscription multiply the number of months by monthly fee for subscription.
One year have 12 months, and 2 years have 2 × 12 = 24 months.
The total cost of subscription = 24 × $16.98 = $407.52
Now find the total cost of a digital video recorder and access to the recording service for 2 years.
$49.99 + $407.52 = $457.51
The offer at DiV would cost $457.51.

TVU
At TVU Mr.Jaros can get free digital video recorder and only would pay 2- year commitment at $19.93.
So, the total cost of a digital video recorder and access to the recording service for 2 years is actually the cost of total 2—years commitment.
To find the total cost of commitment multiply the number of months by monthly fee.
One year has 12 months, and 2 years have 2 × 12 = 24 months.
The total cost of commitment = 24 × $19.95 = $478.8
The offer at TVU would cost $478.8.

The better deal is at DiV, because $457.51 < $478.8.

b. What If? Suppose each offer were for 1 year. Would that change your answer? Explain.
Answer:
Div
To find the total cost of a digital video recorder and access to the recording service for 1 years we have to sum the cost of digital video recorder and the total cost of 1-year subscription.
To find the total cost of subscription multiply the number of months by monthly fee for subscription.
One year has 12 months.
The total cost of subscription = 12 × $16.98 = $203.76
Now find the total cost of a digital video recorder and access to the recording service for 1 years.
$49.99 + $203.76 = $253.75
The offer at DiV would cost $253.75.

TVU
At TVU Mr.Jaros can get free digital video recorder and only would pay 1-year commitment at $19.95.
So, the total cost of a digital video recorder and access to the recording service for 1 years is actually the cost of total 1-years commitment,
To find the total cost of commitment multiply the number of months by monthly fee.
One year has 12 months.
The total cost of commitment = 12 × $19.95 = $239.4
The offer at TVU would cost $239.4.

If the offer were for 1 year, the better deal would be at TVU, because $239.4 < $253.75.

c. Make a Conjecture Find the difference in monthly rates. Divide the cost of the DiV digital video recorder by the difference and round up to the nearest whole number. What does this quotient represent?
Answer:
The difference in monthly rates = $19.95 = $16.98 = $2.97
Now, divide the cost of the DiV digital video recorder by the difference we calculated.
\(\frac{49.99}{2.97}\) = 16.83 ≈ 17
This quotient respresent the number of months.
If the offer were for this number of months, both offers would cost almost the same(because we round up the
quotient to the nearest whole number).
Proof:
DiV
The total cost of subscription = 17 × $16.98 = $288.66
To find the total cost of a digital video recorder and access to the recording service for 17 months we have to sum
the cost of digital video recorder and the total cost of 17 months subscription.
$49.99 + $288.66 = $338.65
TVU
To find the total cost of commitment multiply the number of months by monthly fee.
The total cost of commitment = 17 × $19.95 = $339.15
$338.65 ≈ $339.15

This quotient respresent the number of months. If the offer were for this number of months. Both offers would cost almost the same.

Question 16.
Analyze Relationships Sandy wants to buy 5 pounds of apples. She has a coupon for $1.00 off for every 3 pounds of apples. She gets to the store and discovers that apples are on sale for $0.75 a pound. Is it cheaper for her to buy 5 pounds or 6 pounds? Explain.
Answer:
If Sandy buys 5 pounds of apples. she can use only one coupon for $1 off, because the coupon is valid for every 3 pounds.
The cost of 011e pound of apples is $0.75.
Hence, 5 pounds of apples. without coupon, will cost
5 × $0.75 = $3.75
Now, to find the cost of 5 pounds of apples with a coupon. subtract $1 from $3.75.
$3.75 – $1 = $2.75
Hence, 5 pounds of apples will cost $2.75

If Sandy buys 6 pounds of apples. she can use only two coupon for $1 off, because the coupon is valid for every 3 pounds.
The cost of 0ne pound of apples is $0.75.
Hence, 6 pounds of apples, without coupon, will cost
6 × $0.75 = $4.5
Now, to find the cost of 6 pounds of apples with two coupon, subtract $2(because she can use 2 coupons) from $4.5.
$4.5 – $2 = $2.5
Hence, 6 pounds of apples will cost $2.5

It is cheaper for Sandy to buy 6 pounds of apples. because $2.5 <$2.75.

Question 17.
Draw Conclusions Two stores have a sale on T-shirts originally priced at $8.50. Yeager’s has a “Buy 2, get 1 free” sale. Gample’s has a 30% off sale. Dirk wants to buy only 2 T-shirts. Which is the better buy for him? Explain your reasoning.
Answer:
Yeager ‘s
Yeager’s offer is “3 T-shirts for the price of 2”, ie “buy 2, get 1 free”.
Dirk wants to buy only 2 T-shirts, but buying 2 T-shirts will definitely get a third one.
Let ‘s see how much those 3 shirts would cost.
The price of 1 T-shirt is $8.50, so Dirk would pay for 2 T-shirts, and get a third one for free.
The price of 3 T-shirts = 2 × $8.50 = $17
3 T-shirts would cost $17, but we want to know what is the value of 2 T-shirts.
To find that, divide $17 by 3.
The value of one T-shirt, = \(\frac{\$ 17}{3}\) = $5.67
Time value of 2 T-shirts = 2 × $5.67 = $11.34
The value of 2 T-shirts at Yeager’s is $11.34.

Gample’s

Gamples offer is a discount of 30% on each T—shirt.
Let’s find how much one T-shirt would cost, ie the Discount price.
Discount price = Regular price – Discount
To find the Discount multiply the Regular price by the percent of discount.
The regular price of 1 T-shirt is $8.50.
Write percent as dechnal, ie 30% = 0.30.
Discount = $8.50 × 0.30 = $2.55
[)iscount price = $8.50 – $2.55
Discount price = $5.95
The Discount price of one T-shirt is $5.95.
The Discount price(the value) of 2 T-shirts at Cample’s is 2 × $5.95 = $11.9.

Hence, the better buy for Dirk is at Yeager’s, because the value of 2 T-shirts is less than the value at Gample’s, ie $11.34 < $11.9.

The better buy for Dirk is at Yeager’s, because $11.34 < $11.9.

Question 18.
Represent Real-World Problems Suppose you are buying books from an online store, and the total price of your books is $39. Orders of $50 or more for eligible items qualify for free shipping. Would you buy more to qualify for free shipping? Or would you check out with only the books you have in your shopping cart? Explain your answer.
Answer:
The first question that would come into your mind is, how much is the shipping fee for the books with a total price of $39. If the shipping fee is more than $11, it is better to buy another book which will make the total price at $50. But if the shipping fee is less than $11, lets say $5 and you really don’t have any book to purchase, then you could just pay the shipping fee and your total price will still be less than $50.

It depends on the amount of the shipping fee

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Module 10 Quiz Answer Key.

Texas Go Math Grade 7 Module 10 Quiz Answer Key

Texas Go Math Grade 7 Module 10 Ready to Go On? Answer Key

10.1 Volume of Rectangular Prisms and Pyramids

Find the volume of each figure.

Question 1.

Answer:
l = 11 yd length of base
w = 9 yd Width of base
h = 7 yd Height of a prism
Find the area of the base B. A prism has a base that is rectangular, so use the formula:
B = l.w = 11.9 = 99 yd²
Use the formula for the volume of a rectangular prism.
V = B.h = 99 . 7 = 693 yd³

The volume of a rectangular prism is 693 yd³.

Grade 7 Math Module 10 Answer Key Question 2.

Answer:
l = 12 ft length of base
w = 16 ft Width of base
h = 18 ft Height of a pyramid

Find the area of the base B.

B = l . w = 12 . 16 = 192 ft²
Use the formula for the volume of a rectangular pyramid.

The volume of a rectangular pyramid is 1152 ft³.

The volume of a rectangular pyramid is 1152 ft³.

10.2 Volume of Triangular Prisms and Pyramids

Find the volume of each figure.

Question 3.

Answer:
A prism has a base that is right triangle.
a = 8 cm length of one side of the triangle
b = 17 cm length of other side of the triangle
Find the area of the base B. Use the formula:

B = 68 cm² Base of prism
h = 40 cm Height of a prism
Use the formula.
V = B . h = 68 . 40 = 2720 cm³
The volume of a triangular prism is 2720 cm³.

Module 10 Form B Module Test Answer Key Question 4.

Answer:
b = 5 m length of base
h_B = 15 m height of base
h = 22 m Height of a pyramid
Find the area of the base B. Use the formula:
B = \(\frac{1}{2}\) . b . h_B = \(\frac{1}{2}\) . 5 . 15 = 37.5 m²
Use the formula for the voLume of a triangular pyramid:
V = \(\frac{1}{3}\)B . h = \(\frac{1}{3}\) . (37.5) . 22 = 275 m³
The volume of a triangular pyramid is 275 m³.

10.3 Lateral and Total Surface Area

Find the lateral and total surface area of each figure using its net.

Question 5.

Answer:
Find the Lateral area of the triangular pyramid.
We have three triangles with base of 19.2 m. and height of 40 m.
b = 19.2 m length of base
h_B = 40 m Height of base
Lateral area:

For the area of the base:
b = 24 m length of base
h_b = 15 m Height of base
The area of the base is

The total surface area is 1152 + 180 = 1332 m²

The Lateral area is 1152 m².
The total surface area is 1332 m².

Module 10 Quiz Ready To Go On Answers 7th Grade Question 6.

Answer:
Find the Lateral area of the rectangular prism.
We have:
Two 12 in. by 6 in. rectangle;
Two 10 in. by 6 in. rectangle;
2 . (12 . 6) = 144
2 . (10 . 6) = 120
Lateral area: 144 + 120 = 264 cm²
Each base is 12 in. by 10 in.
2 . (12 . 10) = 2 . 120 = 240 cm²
The total surface area is 264 + 240 = 504 cm².

The Lateral area is 264 cm.
The total surface area is 504 cm².

Essential Question

Question 7.
How can you use volume and surface area to solve real-world problems?
Answer:
Volume and surface area can be used in many ways to solve the real-world problems such as:
For example we are making a new thing of copper and we know the volume of that thing so we can know the exact amount of copper required for making that thing by using the density = \(\begin{gathered}
\text { Mass } \\
\hline \text { Volume }
\end{gathered}\)of copper

In another example suppose a wall is to be painted and the cost of paint one square meter of wall is given then we can easily calculate the total cost for painting wall by using the total surface area of wall.

Volume can be use for calculating amount of material required for making something.

Texas Go Math Grade 7 Module 10 Mixed Review Texas Test Prep Answer Key 

Selected Response

Question 1.
The volume of a triangular pyramid is 232 cubic units. The area of the base of the pyramid is 29 square units. What is the height of the pyramid?
(A) 8 units
(B) 12 units
(C) 16 units
(D) 24 units
Answer:
(D) 24 units

Explanation:
Use formula for the volume of a triangular pyramid.
B = 29 square units Base of pyramid
h = ? Height of a pyramid
V = 232 cubic units The volume of a pyramid
Use the formula for the volume of a pyramid to find a height of the pyramid.
V = \(\frac{1}{3}\) . B . h.
232 = \(\frac{1}{3}\) . 29 . h
232 = (9.66) . h
Divide both sides by 9.66.

The height of the pyramid is 24 units

Question 2.
What is the volume of a rectangular prism that has a length of 8.5 centimeters (cm), a width of 3.2 centimeters, and a height of 6 centimeters?
(A) 19.2 cm³
(B) 27.2 cm³
(C) 51 cm³
(D) 163.2 cm³
Answer:
(D) 163.2 cm³

Explanation:
h = 6 cm Height of prism
l = 8.5 cm Length of base
w = 3.2 cm Width of base
Use the formula for the volume of a rectangular prism
V = B . h = l . w . h
= (8.5) (3.2) . h
= (27.2) . 6
= 163.2 cm³
The volume of a rectangular prism is V = 163.2 cm³

Question 3.
What is the volume of the rectangular pyramid shown?

(A) 1,650 yd³
(B) 2,200 yd³
(C) 3,300 yd³
(D) 6,600 yd³
Answer:
h = 22 yd Height of pyramid
l = 15 yd Length of base
w = 20 yd Width of base
Use the formula for the volume of a rectangular pyramid.
V = \(\frac{1}{3}\) . B . h. = \(\frac{1}{3}\) . l . w . h.
= \(\frac{1}{3}\) . 15 . 20 . 22
= 2200 yd³

The volume of the rectangular pyramid is V = 2200 yd³.

Module 10 Volume Quiz Answer Key Question 4.
A circle has a circumference of 56π centimeters (cm). What is the radius of the circle?
(A) 28 cm
(B) 56 cm
(C) 88 cm
(D) 112 cm
Answer:
(A) 28 cm

Explanation:
Given circumference of circle in probem = 56π cm
We know that circumference of circle of radius “r” = 2π . r
2π . r = 56π (By using above formula)
r = \(\frac{56 \pi}{2 \pi}\) (Dividing both side by 2π)
r = 28 cm (Simplifying)
hence, option A is correct answer.

Question 5.
What is the volume of a triangular prism that has a height of 45 meters and has a base with an area of 20 square meters?
(A) 225 m³
(B) 300 m³
(C) 450 m³
(D) 900 m³
Answer:
(D) 900 m³

Explanation:
h = 45 m Height of a prism
B = 20 m² Base area
Use the formula for the volume of a triangular prism.
V = B . h
= 20 . 45
= 900 m³

The volume of a triangular prism is V = 900 m³.

Question 6.
What is the total surface area of the square pyramid whose net is shown?

(A) 256 in²
(B) 336 in²
(C) 576 in²
(D) 896 in²
Answer:
(C) 576 in²

Explanation:
For lateral area:
There are four triangles with base of 16 in. and height of 10 in.

Lateral area: 320 in²
The base has the shape of 16 in. by 16 in. rectangle.
Base area:
1 (16 . 16) = 256 in²
The total surface area is 320 + 256 = 576 in²

The surface area is 576 in².

Gridded Response

Volume and Surface Area Quiz Answers Module 10 Question 7.
What is the lateral area in square meters of the prism?

Answer:
Lateral area of the prism will be the sum of areas of all the surface except base in the given figure.
Length of the rectangle = 18 in
Breadth of the rectangle = 10 m
Base of the triangle = 12 in
Height of the triangle = 8 in
We know that area of the rectangle is = Length × Breadth
We know that area of the triangle is = \(\frac{1}{2}\) × Base × Height
Area of rectangle = 18 × 10 m²
= 180 m²
Area of triangle = \(\frac{1}{2}\) × 12 × 8 m²
= 48 m²

Lateral area of prism = 2 × Area of rectangle + 2 × Area of triangle
= (2 × 180) + (2 × 48)
= 360 + 96
= 456 m²

Hence, lateral area of the prism is 456 m²

Steps to plot the given box are:
In 1^st column : mark “+” sign
In 2^nd column : mark “0”
In 3^rd coumn: mark “4”
In 4^th column : mark “5”
In 5^th column : mark “6”
In 6^th column : mark “0”
In 7^th column : mark “0”

Lateral area of the prism is 456 m²

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Module 10 Answer Key Volume and Surface Area.

Texas Go Math Grade 7 Module 10 Answer Key Volume and Surface Area

Essential Question
How can you use volume and surface area to solve real-world problems?

Texas Go Math Grade 7 Module 10 Are You Ready? Answer Key

Complete these exercises to review skills you will need for this chapter.

Write a Mixed Number as an Improper Fraction

Example

Write each mixed number as an improper fraction.

Texas Go Math Grade 7 Answers Module 10 Answer Key Question 1.
1\(\frac{9}{10}\) ____
Answer:
Write mixed number as sum of one and his fraction.
1\(\frac{9}{10}\) = 1 + \(\frac{9}{10}\)
centering Write one as
1 + \(\frac{9}{10}\) = \(\frac{10}{10}\) + \(\frac{9}{10}\)
For a sum of this two fractions: Denominator is the same for this two fractions so rewrite it. Numerator is a sum of
both numerators.
\(\frac{10}{10}\) + \(\frac{9}{10}\) = \(\frac{10+9}{10}\) = \(\frac{19}{10}\)

Question 2.
2\(\frac{3}{4}\) ____
Answer:
Write mixed number as a sum of ones and his fraction.
2\(\frac{3}{4}\) = 1 + 1 + \(\frac{3}{4}\)
centering Write one like \(\frac{4}{4}\)
1 + 1 + \(\frac{3}{4}\) = \(\frac{4}{4}\) + \(\frac{4}{4}\) + \(\frac{3}{4}\)
Denominator is the same of this four fractions so rewrite it. Numerator is a sum of numerators of this four fractions.
\(\frac{4}{4}\) + \(\frac{4}{4}\) + \(\frac{3}{4}\) = \(\frac{4+4+3}{4}\)
= \(\frac{11}{4}\)

Question 3.
4\(\frac{1}{6}\) ____
Answer:
Write mixed number as sum of ones and his fraction
4\(\frac{1}{6}\) = 1 + 1 + 1 + 1 + \(\frac{1}{6}\)
centering Write one like \(\frac{6}{6}\).
1 + 1 + 1 + 1 + \(\frac{1}{6}\) = \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{1}{6}\)
Denominator is the same for this five fractions so rewrite it Numerator is a sum of numerators for this five fractions.
\(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{1}{6}\) = \(\frac{6+6+6+6+1}{6}\)
= \(\frac{25}{6}\)

Module 10 Form A Module Test Answer Key Question 4.
7\(\frac{2}{9}\) ____
Answer:
Mixed number write like sum of ones and his fraction

Use Repeated Multiplication

Find each product.

Question 5.
8 × 8 × 8
Answer:

centering Find a product of two numbers on the box
8 . 8 = 64
centering Multiply the result by the third number
64 . 8 = 512

Question 6.
5 × 5 × 5
Answer:

centering Multiply the first two numbers.
5 . 5 = 25
centering Multiply the result by the third number
25 . 5 = 125

Surface Area Texas Module 10 Go Math Question 7.
5.1 × 5.1 × 5.1
Answer:
Multiply the first two numbers

Multiply the result by the third number.

132.651 ≈ 132.7

Question 8.
4 × 4 × 4 × 4
Answer:

centering Find a product of two number on the box.
4 . 4 = 16
centering Multiply the result by the third number
16 . 4 = 64

Multiply Fractions

Multiply. Write each product in simplest form.

Question 9.
\(\frac{1}{2}\) × \(\frac{1}{3}\)
Answer:
Multiply numerator with numerator and denominator with denominator.
\(\frac{1}{2}\) . \(\frac{1}{3}\) = \(\frac{1 \cdot 1}{2 \cdot 3}\)
= \(\frac{1}{6}\)

Question 10.
\(\frac{3}{4}\) × \(\frac{5}{6}\)
Answer:
Multiply numerator with numerator and denominator with denominator.

Module 10 Form B Module Test Answer Key Question 11.
\(\frac{9}{10}\) × \(\frac{15}{16}\)
Answer:
Multiply numerator with numerator and denominator with denominator.

Question 12.
\(\frac{2}{5}\) × \(\frac{5}{12}\)
Answer:
Multiply numerator with numerator and denominator with denominator.

Question 13.
\(\frac{4}{7}\) × \(\frac{3}{16}\)
Answer:
Multiply numerator with numerator and denominator with denominator.

Question 14.
\(\frac{5}{12}\) × \(\frac{3}{20}\)
Answer:
Multiply numerator with numerator and denominator with denominator.

Question 15.
\(\frac{3}{8}\) × \(\frac{3}{5}\)
Answer:
Multiply numerator with numerator and denominator with denominator
\(\frac{3}{8}\) . \(\frac{3}{5}\) = \(\frac{3 \cdot 3}{8 \cdot 5}\)
= \(\frac{9}{40}\)

Module 10 Mathematics Grade 7 Answer Key Question 16.
\(\frac{5}{9}\) × \(\frac{7}{10}\)
Answer:
Multiply numerator with numerator and denominator with denominator.

Texas Go Math Grade 7 Module 10 Reading Start-Up Answer Key

Visualize Vocabulary
Use the ✓’ words to complete the graphic. You will put one word in each oval.

Understand Vocabulary

Match the term on the left to the correct expression on the right.

Answer:
1. Lateral faces – Parallelograms that form the sides of a prism and connect the bases.
2. Surface area – The sum of alt of the areas of all of faces of a prism.
3. Lateral area – The sum of the areas of all lateral faces in a prism.

Active Reading

Booklet Before beginning the module, create a booklet to help you learn the concepts in this module. Write the main idea of each lesson on one page of the booklet. As you study each lesson, write important details that support the main idea, such as vocabulary and formulas. Refer to your finished booklet as you work on assignments and study for tests.

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 10.3 Answer Key Lateral and Total Surface Area.

Texas Go Math Grade 7 Lesson 10.3 Answer Key Lateral and Total Surface Area

Example 1
A net of a rectangular prism is shown. Use the net to find the lateral area and the total surface area of the prism. Each square represents one square inch. The blue regions are the bases, and the green regions are the lateral faces.

Step 1
Find the lateral area of the rectangular prism. There are two 2 in. by 5 in. rectangles, and two 2 in. by 6 in. rectangles.

2 . (2 . 5) = 20 in²
2 . (2 . 6) = 24 in²
The lateral area is 20 + 24 = 44 in².

Step 2
Find the total surface area of the rectangular prism.
Each base is 5 inches by 6 inches. 2 . (5 . 6) = 60 in².
The total surface area is 44 + 60 = 104 in².

Math Talk
Mathematical processes
Explain how the total surface area of a prism differs from the lateral area.

Your Turn

7th Grade Go Math Answer Key Lesson 10.3 Question 1.
Use the net to find the lateral area and the total surface area of the triangular prism described by the net.

Answer:
Find the Lateral area of the triangular prism. We have:
One 4 cm. by 4 cm. rectangle;
One 4 cm. by 5 cm. rectangle;
One 3 cm. by 4 cm. rectangle.
1 . (4 . 4) = 16
1 . (4 . 5) = 20
1 . (3 . 4) = 12
The lateral area is 16 + 20 + 12 = 48 cm².
Each base is 4 cm. by 3 cm.\
2 . (4 . 3) = 2 . 12 = 24 cm²
The total surfance area is 48 – 24 = 72 cm².

Example 2
Use the net of this rectangular pyramid to find the lateral area and the total surface area of this pyramid.

Step 1
Find the lateral area of the rectangular pyramid. There are four triangles with base 16 in. and height 17 in. The lateral area is 4 × \(\frac{1}{2}\)(16)(17) = 544 in².

Step 2
Find the total surface area of the rectangular pyramid.
The area of the base is 16 × 16 = 256 in².
The total surface area is 544 + 256 = 800 in².

Reflect

Question 2.
How many surfaces does a triangular pyramid have? What shape are they?
Answer:
A triangular pyramid has four surfaces and they have the shape of triangle.

Your Turn

Question 3.
The base and all three faces of a triangular pyramid are equilateral triangles with side lengths of 3 ft. The height of each triangle is 2.6 ft. Use the net to find the lateral area and the total surface area of the triangular pyramid.

Answer:
Find the lateral area of the triangular pyramid.
We have three equilateral triangles with base 3 ft. and height 17 ft.
b = 3 ft Length of base
h_B = 2.6 ft Height of base
Lateral area:
3 . (\(\frac{1}{2}\) . b . h_b) = 3 . \(\frac{1}{2}\) . 3 . (2.6) = 11.7 ft²
The base is the same triangle as triangles in lateral faces of a triangular pyramid
Therefore, area of the base is: \(\frac{1}{2}\) . b . h_b = 3.9 ft
The total surface area is 11.7 + 3.9 = 15.6 ft².
The lateral area is 11.1 ft².
The total surface area is 15.6 ft².

Go Math Grade 7 Lesson 10.3 Answer Key Question 4.
Use a net to find the lateral area and the total surface area of the pyramid.

Answer:
Find the Lateral area of the rectangular pyramid.
We have four triangles with base 16 in. and height 20 in.
b = 16 ft Length of base
h_B = 20 ft Height of base
Lateral area:
4. (\(\frac{1}{2}\) . b. h_b) = 4 . \(\frac{1}{2}\) . 16 . 20 = 640 in²
The base is in the shape of rectangle.
Therefore, area of the base is: b . b = 256 in
The total surface area is 640 + 256 = 896 in²
The lateral area is 640 in².
The total surface area is 896 in².

Example 3.
Shoshanna’s team plans to build stands to display sculptures. Each stand will be in the shape of a rectangular prism. The prism will have a square base with side lengths of 2\(\frac{1}{2}\) feet, and it will be 3\(\frac{1}{2}\) feet high. The team plans to cover the stands with metallic foil that costs $0.22 per square foot. How much money will the team save on each stand if they cover only the lateral area instead of the total surface area?

Step 1
Make a net of the rectangular prism.

Step 2
Find the lateral and total surface areas of the prism.
The four lateral faces are 3\(\frac{1}{2}\) feet by 2\(\frac{1}{2}\) feet rectangles. The two bases are 2\(\frac{1}{2}\) feet by 2\(\frac{1}{2}\) feet squares.
Lateral area: 4\(\frac{1}{2}\) . (3\(\frac{1}{2}\) . 2\(\frac{1}{2}\)) = 35 square feet
Total surface area: 2 (2\(\frac{1}{2}\) . 2\(\frac{1}{2}\)) + 35 = 47\(\frac{1}{2}\) square feet

Add the area of the bases to the lateral area.

Step 3
Find and compare the prices.
Cost for total surface area: $0.22(47\(\frac{1}{2}\)) = $10.45
Cost for lateral area: $0.22(35) = $7.70
The team will save $10.45 – $7.70, or $2.75, for each stand by covering only the lateral area.

Your Turn

Question 5.
Kwame’s team will make two triangular pyramids to decorate the entrance to the exhibit. They will be wrapped in the same metallic foil. Each base is an equilateral triangle. If the base has an area of about 3.9 square feet, how much will the team save altogether by covering only the lateral area of the two pyramids?
The foil costs $0.22 per square foot. _______

Answer:
Find the lateral area of the triangular pyramid
We have three triangles with base of 3 ft and height of 6.1 ft.
b = 3 ft Length of base
h_B = 6.1 ft Height of base
Lateral area:
3. (\(\frac{1}{2}\) . b. h_b) = 3 . \(\frac{1}{2}\) . 3. (6.1) = 27.45 ft²
Base area:
B = 3.9 ft²
If they cover both whole pyramids they will spend:
2 (27.45 + 3.9) = 62.7 ft^2<
If we cover the lateral area of two pyramids we will spend:
2 . (27.45) = 54.9 ft²
The team will save:
0.22. (62.7 – 54.9) = 0.22. 7.8 = $1.7
The team will save $1.7

Texas Go Math Grade 7 Lesson 10.3 Guided Practice Answer Key 

A three-dimensional figure is shown sitting on a base. (Example 1)

Question 1.
The figure has a total of _____ rectangular faces.
Answer:
The figure has a total of six rectangular faces.

Question 2.
Of the total number of faces, ___ are lateral faces.
Answer:
Of the total number of faces, four are lateral faces

Question 3.
The figure is a ____.
Answer:
The figure is a rectangular prism

Go Math 7th Grade Practice and Homework Lesson 10.3 Answer Key Question 4.
Sketch a net of the figure.
Answer:

Each box in the figure represent a single unit.

Question 5.
The lateral area of the prism is ___.
Answer:
For lateral area:
Two 6 by 3 rectangtes
Two 7 by 3 rectangles.
2 . (6 . 3) = 36
2 . (7 . 3) = 42
Lateral area: 36 + 42 = 78

The lateral area of the prism is
36 + 42 = 78

Question 6.
The total surface area is ___.
Answer:
The base is in the shape of 6 by 7 rectangle.
Base area: 2 (6 . 7) = 84
The total surface area is 78 + 84 = 162

A triangular prism is shown. (Example 2)

Question 7.
Identify the number and type of faces of the prism.
Answer:
A triangular prism has five face:
Two 6 cm. by 4.3 cm. rectangles;
One 6 cm. by 3 cm. rectangle;
Two triangles with base of 3 cm. and height of 4 cm.

Question 8.
Find the lateral area of the prism. ____
Answer:
For lateral area:
Two 6 cm. by 4.3 cm. rectangles;
One 6 cm. by 3 cm. rectangle;
2 . (6 . (4.3)) = 51.6
1 . (6 . 3) = 18
Lateral area: 51.6 + 18 = 69.6 cm².

The lateral area of the prism is 69.6 cm².

Question 9.
Find the total surface area of the prism.
Answer:
The base is in the shape of triangle with length of 3 cm. and height of 4 cm.
Base area 2 . (\(\frac{1}{2}\) . 3 . 4) = 12 ft²
The total surface area is 69.6 + 12 = 81.6 cm².

Go Math Lesson 10.3 7th Grade Areas of Similar Shapes Answer Key Question 10.
Use a net to find the total surface area of the pyramid. Then find the cost of wrapping the pyramid completely in gold foil which costs $0.05 per square centimeter. (Examples 2 and 3)
Answer:
Find the lateral area of the rectangular pyramid.
we have four triangles with base of 10 cm. ain height of 12 cm.
b = 10 cm Length of base
h_B = 12 cm Height of base
Lateral area:
4 . (\(\frac{1}{2}\) . b . h_b) = 4 . \(\frac{1}{2}\) . 10 . 12 = 240 cm²
Base area:
10 . 10 = 1oo cm²
The total surface area is 240 + 100 = 340 cm².
Wrapping the pyramid completely in gold foil will cost: 340 . (0.05) = $17

Essential Question Check-In

Question 11.
How do you find the lateral and total surface area of a triangular pyramid?
Answer:
Lateral surface area of any three-dimensional figure means the sum of area of all sides except the area of base. And the total surface area means the area of all the sides of figure including the area of base.

Now in case of triangular pyramid it will have total four faces including the base triangle. So the lateral surface area will. be the sum of areas of all the three triangle which are faces of triangular pyramid except the base triangle. And the total surface area will be the sum of areas of all the four triangle including the base triangle

Texas Go Math Grade 7 Lesson 10.3 Independent Practice Answer Key 

Question 12.
Use a net to find the lateral area and the total surface area of the cereal box.
Lateral area: __________________________
Total surface area: _____________________

Answer:
The cereal box is in the shape of a rectangular prism.
Find the lateral area of the rectangular prism.
We have:
Two 2 in. by 12 in. rectangles;
Two 8 in. by 12 in. rectangles;
2 . (2 . 12) = 2 . 24 = 48
2 . (8 . 12) = 2 . 96 = 192
Lateral area: 48 – 192 = 240 in².
Each base is 8 in. by 2 in.\
2 . (8 . 2) = 2 . 16 = 32 in²
The total surface area is 240 + 32 = 272 in².
The lateral area is 240 in².
The total surface area is 272 in².

Question 13.
Describe a net for the shipping carton shown.
Answer:
Net of the given rectangular prism or cuboid will consist of six rectangular surface with front and behind rectangle having dimension of 8 inch by 12 inch. And the dimension of top and bottom rectangle will be 8 inch by 2 inch.

Net of the given figure will consist of 6 rectangular surface.

Question 14.
A shipping carton is in the shape of a triangular prism.
Use a net to find the lateral area and the total surface area of the carton.
Lateral area: __________________________
Total surface area: _____________________

Answer:
Find the lateral area of the triangular prism.
We have:
Two 3.6 in. by 15 in. rectangles;
One 4 in. by 15 in. rectangles.
2. ((3.6) . 15) = 2 . 54 = 108
1 . (4 . 15) = 1 . 60 = 60
Lateral area: 108 + 60 = 168 in²
Each base has the shape of triangle with length of 8 in. and height of 12 in.

Base Area
2 . 48 = 96 in²
The total surface area is 168 + 96 = 264 in².

The lateral area of the carton is 168 in².
The total surface area of the carton is 264 in².

Question 15.
Victor wrapped this gift box with adhesive paper (with no overlaps). How much paper did he use?
Answer:
The gift box is in the shape of a rectangular prism.
Find the lateral area of the rectangular prism.
We have:
Two 6 in. by 5 in. rectangle;
Two 8 in. by 5 in. rectangle.
2 . (6 . 5) = 60
2 . (8 . 5) = 80
The lateral area is 60 + 80 = 140 in².
Each base is 8 in. by 6 in.\
2 . (8 . 6) = 2 . 48 = 96 in²
The total surfance area is 140 + 96 = 236 in².

He used 236 in² of paper.

Question 16.
Vocabulary Name a three-dimensional shape that has four triangular faces and one rectangular face.
Answer:
Three-dimensional The shape that has four triangular faces and one rectangular face is a rectangular pyramid

Go Math 7th Grade Lesson 10.3 Answer Key Question 17.
Cindi wants to cover the top and sides of this box with glass tiles that are 1 cm square. How many tiles will she need?

Answer:
The box is in the shape of a rectangular prism.
Find the lateral area.
Two 15 cm. by 9 cm. rectangLe,
Two 20 cm. by 9 cm. rectangle;
2 . (15 . 9) = 270
2 . (20 . 9) = 360
Lateral area: 270 + 360 = 630 cm².
The base is 20 cm. by 15 cm.
To cover a top of box we need a surface of one base.
1 . (20 . 15) = 1 . 300 = 300 cm²
To cover a top and sides of this box Cindi needs 630 + 300 = 930 cm².
Therefore, she needs 930 tiles.
Cindi needs 930 tiles

Question 18.
A glass paperweight has the shape of a triangular prism. The bases are equilateral triangles with side lengths of 4 inches and heights of 3.5 inches. The height of the prism is 5 inches. Find the lateral area and the total surface area of the paperweight.
Answer:
For lateral area:
There are three 4 in. by 5 in. rectangles.
3 . (4 . 5) = 3 . 20 = 60 in²
Lateral area: 60 in²
Base area:
The bases are equilateral triangles with length of 4 in. and height of 3.5 in.
2 . (\(\frac{1}{2}\) . 4 . (3.5)) = 14 in²
The total surface area is 60 + 14 = 74 in².

Lateral area: 60 in².
The total surface area is 74 in².

Question 19.
The doghouse shown has a floor, but no windows. Find the total surface area of the doghouse (including the door).

Answer:
Base of doghouse is in the shape of a rectangular prism.
For lateral area:
Two 4 ft. by 2 ft rectangles;
Two 3 ft by 2 ft. rectangles;
2 . (4 . 2) = 16
2 . (3 . 2) = 12
Lateral area: 16 + 12 = 28 ft².
The base has the shape of rectangle 3 ft by 4 ft
Base area: 1 . (3 . 4) = 24 ft²
The total surface area is 28 + 24 = 52 ft².
The roof of a doghouse is in the shape of triangular pyramid.
For lateral area:
Two 2.5 ft. by 4 ft. rectangles;
One 3 ft by 4 ft. rectangle.
2 . (2.5 . 4) = 20
1. (3 . 4) = 12
Lateral area: 20 + 12 = 32 ft².
The base has the shape of triangle with length of 3 ft and height of 2 ft.
Base area:
2 . (\(\frac{1}{2}\) . 3 . 2) = 6 ft²
The total surface area is 32 + 6 = 38 ft².
The total surface area of the doghouse is:
52 + 38 = 90 ft²

The total surface area of the doghouse is 90 ft².

Question 20.
Describe the simplest way to find the total surface area of a cube.
Answer:
The surface area of a cube is the area of the six squares that cover it. The area of one of them is b. b. Since these are alt the same, multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.

Lesson 10.3 Answer Key 7th Grade Go Math Question 21.
Communicate Mathematical Ideas Describe how you approach a problem involving lateral area and total surface area. What do you do first? In what ways can you use the figure that is given with a problem? What are some shortcuts that you might use when you are calculating these areas?
Answer:
When solving a problem involving lateral area and total surface area, determine first the lateral area of the given
figure. This is because the lateral area is needed to determine the total surface area of the given figure. It is easier to determine the lateral area of the given figure if you know what figure are you dealing with, is it a pyramid or a prism, and what is the base of the given figure. The total surface area is the sum of the lateral area and the area of the base. The lateral area should be determined first before determining the total surface area of the given figure.

Solve for the lateral area first.

Texas Go Math Grade 7 Lesson 10.3 H.O.T. Focus on Higher Order Thinking Answer Key 

Question 22.
Persevere in Problem-Solving A pedestal in a craft store is in the shape of a triangular prism. The bases are right triangles with side lengths of 12 cm, 16 cm, and 20 cm. The store owner used 192 cm² of burlap cloth to cover the lateral area of the pedestal. Find the height of the pedestal.
Answer:
Lateral area:
One 20 cm. by h cm. rectangle;
One 12 cm. by h cm. rectangle;
One 16 cm. by h cm. rectangle.
1 . (20 . h) = 20 . h.
1 . (12 . h) = 12 . h.
1 . (16 . h.) = 16 . h.
Lateral area: 20 . h. + 12 . h + 16 . h = 48 . h cm².
The lateral area is 192 cm².
192 = 48 . h.
Divide both sides by 48.

The height of the pedestal is h = 4 cm.

Question 23.
Communicate Mathematical Ideas The base of Prism A has an area of 80 ft², and the base of Prism B has an area of 80 ft². The height of Prism A is the same as the height of Prism B. Is the base of Prism A congruent to the base of Prism B? Explain.
Answer:
The base of Prism A has the same area as the base of Prism B. They could be congruent however, it depends on the shape of the base. If the bases of Prism A and Prism B are both squares, then they are congruent. But if the bases of Prism A and Prism B are triangles or rectangles, there could be a difference in the dimensions of the triangle base and the rectangle base, which makes them not congruent It is because congruent figures have the same shape and size.

It depends on the shape of the base.

Question 24.
Critique Reasoning A triangular pyramid is made of 4 equilateral triangles. The sides of the triangles measure 5 m, and the height of each triangle is 4.3 m. A rectangular prism has a height of 4.3 m and a square base that is 5 m on each side. Susan says that the total surface area of the prism is more than twice the total surface area of the pyramid. Is she correct? Explain.
Answer:
Triangular pyramid:
For lateral area:
We have three triangles with a base of 5 m. and height of 4.3 m.
b = 5m Length of base
h_B = 4.3 m Height of base
Lateral area:
3. (\(\frac{1}{2}\). b . h_b) = 3 . \(\frac{1}{2}\) . 5 . (4.3) = 32.25 m²
Lateral area: 32.25 m².
The base is in the shape of a triangle with a base of 5 m. and height of 4.3 m
Base area: 1 . (\(\frac{1}{2}\) . 5. (4.3)) = 10.75 m²
The total surface area is 32.25 + 10.75 = 43 m²
Rectangular prism:
For lateral area:
We have four 5 m. by 4.3 m. rectangles.
4 . (5 . (4.3)) = 86
Lateral area: 86 m²
The base is in the shape of 5 m. by 5 m. rectangle.
Base area:
2 (5 . 5) = 50 m²
The total surface area is 86 + 50 = 136 m².

Susan is correct. The total surface area of the prism is three times of total surface area of the pyramid.

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 11.2 Answer Key Comparing Data Displayed in Dot Plots.

Texas Go Math Grade 7 Lesson 11.2 Answer Key Comparing Data Displayed in Dot Plots

Essential Question
How do you compare two sets of data displayed in dot plots?

Texas Go Math Grade 7 Lesson 11.2 Explore Activity Answer Key  

Analyzing Dot Plots
You can use dot plots to analyze a data set, especially with respect to its center and spread.

People once used body parts for measurements. For example, an inch was the width of a man’s thumb. In the 12th century, King Henry I of England stated that a yard was the distance from his nose to his outstretched arm’s thumb. The dot plot shows the different lengths, in inches, of the “yards” for students in a 7th grade class.

A. Describe the shape of the dot plot. Are the dots evenly distributed or grouped on one side?

B. What value best describes the center of the data? Explain how you chose this value.

C. Describe the spread of the dot plot. Are there any outliers?

Reflect

Lesson 11.2 Comparing Data Displayed in Dot Plots Answer Key Question 1.
Calculate the mean, median, and range of the data in the dot plot.
Answer:
To find the mean, add the numbers and divide the sum by the number of addends.
28 + 29 + 29 + 30 + 30.5 + 30.5 + 31 + 31 + 31 + 31.5 + 31.5 + 32 + 32 + 32.5 + 32.5 + 33 + 33 + 33.5 + 34 + 34 + 35 = 664.5
\(\frac{664.5}{21}\) = 31.64
Mean is 31.64
The median is the middle number of the data in the dot plot that is ordered from least to greatest

Range is the difference between the greatest and least number of the data in the dot plot
range = 35 – 28 = 7

Mean : 31.64
Median : 31.7
Range : 7

Comparing Dot Plots Visually
You can compare dot plots visually using various characteristics, such as center, spread, and shape.

Example 1.
The dot plots show the heights of 15 high school basketball players and the heights of 15 high school softball players.

A. Visually compare the shapes of the dot plots.
Softball: All the data is 5’6” or less.
Basketball: Most of the data is 5’8” or greater.
As a group, the softball players are shorter than the basketball players.

B. Visually compare the centers of the dot plots.
Softball: The data is centered around 5’4’
Basketball: The data is centered around 5’8’
This means that the most common height for the softball players is 5 feet 4 inches, and for the basketball players 5 feet 8 inches.

C. Visually compare the spreads of the dot plots.
Softball: The spread is from 4’11 “to 5’6”.
Basketball: The spread is from 5’2” to 6’0’
There is a greater spread in heights for the basketball players.

Math Talk
How do the heights of field hockey players compare with the heights of softball and basketball players?

Your Turn

Question 2.
Visually compare the dot plot of heights of field hockey players to the dot plots for softball and basketball players.
Shape: _______________
Center: _______________
Spread: _______________
Answer:
Shapes:
Hockey: All the data is 5’6” or less.
The hockey players are shorter than the basketball players, but taller than the softball players.
Center:
Hockey: The data is centered around of 5’2”.
Spread:
Hockey: The spreads is from 4’9” to 5’6”.
They have same spread as spread for softball players, but there is a greater spread in heights for the basketball players.

All the data is 5’6″ or Less.
The data is centered around of 5’2”.
The spreads is from 4’9” to 5’6″.

Comparing Dot Plots Numerically
You can also compare the shape, center, and spread of two dot plots numerically by calculating values related to the center and spread. Remember that outliers can affect your calculations.

Example 2
Numerically compare the dot plots of the number of hours a class of students exercises each week to the number of hours they play video games each week.

A. Compare the shapes of the dot plots.
Exercise: Most of the data is less than 4 hours.
Video games: Most of the data is 6 hours or greater.

B. Compare the centers of the dot plots by finding the medians.
Median for exercise: 2.5 hours. Even though there are outliers at
12 hours, most of the data is close to the median.
Median for video games: 9 hours. Even though there is an outlier at 0 hours, these values do not seem to affect the median.

C. Compare the spreads of the dot plots by calculating the range.
Exercise range with outlier: 12 – 0 = 12 hours
Exercise range without outlier: 7 – 0 = 7 hours
Video games range with outlier: 14 – 0 = 14 hours
Video games range without outlier: 14 – 6 = 8 hours

Math Talk
Mathematical Processes
How do outliers affect the results of this data?

Your Turn

Comparing Data Displayed in Box Plots Lesson 11.2 Answer Key Question 3.
Calculate the median and range of the data in the dot plot. Then compare the results to the dot plot for Exercise in Example 2.

Answer:
Median for Internet Usage: 6 hours
Most of the data is close to the median
Median for Exercise: 2.5 hours
Internet Usage range with outliers: 11 – 1 = 10 hours
Internet usage range without outliers: 8 – 4 = 4 hours
Exercise range with outlier: 12 hours
Exercise range without outlier: 7 hours

Median for Internet Usage : 6 hours
Internet Usage range:

1. With outliers: 10 hours
2. Without outliers: 4 hours

Texas Go Math Grade 7 Lesson 11.2 Guided Practice Answer Key

The dot plots show the number of miles run per week for two different classes. For 1-5, use the dot plots shown.

Question 1.
Compare the shapes of the dot plots.
Answer:
Class A: Most of the the data is 6 mi. or less.
Class B: All the data is 3 mi. or greater
As a class, Students from Class A run more than students from Class B

Class A: Most of the the data is 6 mi. or less.
Class B: All the data is 3 mi. or greater
As a class, Students from Class A run more than students from Class B.

Question 2.
Compare the centers of the dot plots.
Answer:
Class A: The data is centred around 4 mi.
Class B: The data is centered around 7 mi.

Question 3.
Compare the spreads of the dot plots.
Answer:
Class A: The spread is from 4 mi. to 14 mi
Class B: The spread is from 3 mi. to 9 mi.

Go Math 7th Grade Practice and Homework Lesson 11.2 Answer Key Question 4.
Calculate the medians of the dot plots.
Answer:

Median for Class A: 7.5 mi.
Median for Class B: 5.75 mi.

Question 5.
Calculate the ranges of the dot plots.
Answer:
Class A range with outliers: 14 – 4 = 10 mi
Class A range without outliers: 6 – 4 = 2 mi
Class B range: 9 – 3 = 6 mi
For Class B the outlier doesn’t exist.

Class A range with outliers: 10 mi
Class A range without outliers: 2 mi
Class B range: 6 mi
For Class B the outlier doesn’t exist.

Essential Question Check-In

Question 6.
What do the medians and ranges of two dot plots tell you about the data?
Answer:
The medians of any data represents the centre or almost centre point of the given data. So in above two dot plots
the medians tells that which of the given dots have higher value. And the range of any data set represent the value around which all the data are spread. So in second dot plot the dots are very close as compared to first dot plot which means in second dot plots the value of data are closer.

Median of any data represent centre value.

Texas Go Math Grade 7 Lesson 11.2 Independent Practice Answer Key

The dot plot shows the number of letters in the spellings of the 12 months. Use the dot plot for 7-10.

Question 7.
Describe the shape of the dot plot.
Answer:
All of the data are 3 letters or more.

Go Math 7th Grade Lesson 11.2 Independent Practice Answer Key Question 8.
Describe the center of the dot plot.
Answer:
The data are centered around 8 letters.

Question 9.
Describe the spread of the dot plot.
Answer:
The spread is from 3 to 9 letters.

Question 10.
Calculate the mean, median, and range of the data in the dot plot.
Answer:

Mean: 6.16 letters
Median: 6 Letters
Range: 6 Letters

The dot plots show the mean number of days with rain per month for two cities.

Question 11.
Compare the shapes of the dot plots.
Answer:
Number of Days of rain for Montogomery, AL: All of the data is 12 days or less.
Number of Days of rain for Lynchburg, VA: All of the data is 8 days or more.
There are more days of rain in Lynchburg than in Montogomery.

Question 12.
Compare the centers of the dot plots.
Answer:
Montgomery: The data is centered around 8 days
Lynchburg: The data is centered around 10 days.

Question 13.
Compare the spreads of the dot plots.
Answer:
Montgomery: The spread is from 1 day to 12 days.
Lynchburg: The spread is from 8 days to 12 days.

Go Math Lesson 11.2 Answer Key Compare Dot Plots Question 14.
What do the dot plots tell you about the two cities with respect to their average monthly rainfall?
Answer:
The dot plot for Montgomery, AL showed that the average monthly rainfall in their city is inconsistent. The dot plot showed that there are days when the rainfall is heavy then it changes. Also, there is an outlier which made it more inconsistent For Lynchburg, VA, the average monthly rainfall in their city is somewhat consistent. Also, the days were relatively closer.

The average monthly rainfall in Lynch burg, VA is more consistent compared to Montgomery, AL.

The dot plots show the shoe sizes of two different groups of people.

Question 15.
Compare the shapes of the dot plots.
Answer:
Group A: All of the data is 65 or greater
Group B: All of the data is 8.5 or greater.
Group B has greater sizes of shoe than Group A.

Question 16.
Compare the medians of the dot plots.
Answer:
Median for Group A: 8 size of shoe
Median for Group B:

Median for Group A: 8 size of shoe
Median for Group B: 9.71 size of shoe

Question 17.
Compare the ranges of the dot plots (with and without the outliers).
Answer:
Group A range with outliers: 13 – 6.5 = 6.5 size of shoe
Group A range without outliers: 9 – 6.5 = 2.5 size of shoe
Group B range with outliers: 11.5 – 8.5 = 3 size of shoe
Group B range without outliers: 11.5 – 8.5 = 3 size of shoe

Group A range with outliers is 65 size of shoe
Group A range without outliers is 2.5 size of shoe
Group B range with outliers is 3 size of shoe
Group B range without outliers is 3 size of shoe

Question 18.
Make A Conjecture Provide a possible explanation for the results of the dot plots.
Answer:
Group A probably consists mostly of younger people and/or women (who tends to have smaller feet). Group B, on
the other hand, consists mostly of adults (who tends to have bigger feet).

Group A consists of younger people while Group B consists of adults.

Texas Go Math Grade 7 Lesson 11.2 H.O.T. Focus On Higher Order Thinking Answer Key

Question 19.
Analyze Relationships Can two dot plots have the same median and range but have completely different shapes? Justify your answer using examples.
Answer:
Yes, two dot plots can have the same median and range but completely different shapes.
In both the given dot plot the median is 6th term which is 7 and also the range of both dot plot is 7.

Dot plot of type A data is shown below:

Dot plot of type B data is shown below:

Yes, two dot plots can have the same median and range.

Comparing Dot Plots Answer Key Go Math Lesson 11.2 Question 20.
Draw Conclusions What value is most affected by an outlier, the median or the range? Explain. Can you see these effects in a dot plot?
Answer:
The range is the most affected by an outlier.
This can be understood by the example given below:
For example the data of the sample are 3, 5, 5, 5, 7, 8, 8, 9, 10, 12, 15.
Median = 6th term of data
= 8
Range = 15 – 3
= 12
New sample after excluding outlier: 3, 5, 5, 5, 7, 8, 8, 9, 10, 12.

Range = 12 – 3
= 9
Here we can see that the median decreases by only 0.5 but the range decreases by 3. Hence we can see that the range is most affected by outliers.

The range is most affected by outlier

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 10.1 Answer Key Volume of Rectangular Prisms and Pyramids.

Texas Go Math Grade 7 Lesson 10.1 Answer Key Volume of Rectangular Prisms and Pyramids

Texas Go Math Grade 7 Lesson 10.1 Example Answer Key  

Example 1.
Find the volume of the rectangular prism.

Step 1
Find the area of the base.
B = lw Use the formula.
B = 12 × 15 Substitute for l and w.
B = 180 mm²

Step 2
Find the volume.
V= Bh Use the formula.
V = 180 × 7 Substitute for sand h.
V = 1,1260 mm³
The volume of the rectangular prism is 1,260 cubic millimeters.

Reflect

Lesson 10.1 Volume of Prisms and Cylinders Answer Key Question 1.
What If? If you know the volume V and the height h of a prism, how would you find the area of the base B?
Answer:
The volume V of a prism is the area of its base B times its height h.
V = B.h…(1)
We know the volume V and the height of a prism.
Divide (1) by h.

We find the area of the base B as \(\frac{V}{h}\) = B

Your Turn

Question 2.
Use the formula V = Bh to find the volume of a gift box that is 3.5 inches high, 7 inches long, and 6 inches wide.
Answer:
The volume V of a prism is the area of its base B times its height h.
V = B . h The volume of a prism
h = 3.5 Height of a prism
w = 6 Width of base
l = 7 Lenght of base

Find the area of the base.
B = w . l = 6 . 7 = 42 in²

Find the volume.

V = B . h = 42 . (3.5) = 147 m³
The volume V of a prism is V = 147 in³.

Texas Go Math Grade 7 Lesson 10.1 Explore Activity Answer Key  

Nets
A net is a two-dimensional pattern of shapes that can be folded into a three-dimensional figure. The shapes in the net become the faces of the three-dimensional figure.

Step 1
Copy Net A and Ñet B on graph paper, and cut them out along the blue lines.

One of these nets can be folded along the black lines to make a cube. Which net will not make a cube? _________________

Step 2
See if you can find another net that can be folded into a cube.
Draw a net that you think will make a cube on your graph paper, and then cut it out. Can you fold it into a cube? Sketch your net below.

Step 3
Compare your results with several of your classmates. How many different nets for a cube did you and your classmates find?

Reflect

Question 3.
What shapes will appear in a net for a rectangular prism that is not a cube? How many of these shapes will there be?
Answer:
A rectangular prism is a three-dimensional shape with six rectangular-shaped sides, so will appear as six rectangles.

How do you know that each net cannot be folded into a cube without actually cutting and folding it?

Question 4.

Answer:
This net cannot be folded in the shape of a cube because a cube is a three-dimensional figure with six equal square faces. The net is missing one square

7th Grade Volume Rectangular Prism Answer Key  Question 5.

Answer:
This net cannot be folded in the shape of a cube because a cube is a three-dimensional figure with six equal square faces. In this net the squares overlap.

Question 6.
Make a Conjecture If you draw a net for a cylinder, such as a soup can, how many two-dimensional geometric shapes would this net have? Name the shapes in the net for a cylinder.
Answer:
It will be three two-dimensional shapes; one rectangle and two circles

Exploring the Volume of a Rectangular Pyramid

A pyramid is a three-dimensional shape whose base is a polygon and whose other faces are all triangles. Like a prism, a pyramid is named by the shape of its base.

The faces of a pyramid that are not the base have a common vertex, called the vertex of the pyramid. The perpendicular distance from the vertex to the base is the height of the pyramid.

Explore Activity 2
In this activity, you will compare the volumes of a pyramid and a prism with congruent bases and equal heights. Remember that congruent figures have the same shape and size.

Step 1
Make three-dimensional models. Make larger versions of the nets shown. Make sure the bases and heights in each net are the same size. Fold each net, and tape it together to form a prism or a pyramid.

Step 2
Fill the pyramid with beans. Make sure that the beans are level with the opening of the pyramid. Then pour the beans into the prism. Repeat until the prism is full. How many times did you fill the prism from the pyramid? __________________________

Step 3
Write a fraction that compares the volume of the pyramid to the volume of the prism.

Math Talk
Mathematical Processes
Describe ways in which a prism and a pyramid are different.

Reflect

Question 7.
Draw Conclusions A rectangular pyramid has a base of B and a height of h. What is a formula for the volume of the pyramid? Justify your reasoning.
Answer:
Given base area of the rectangular Pyramid = B
Given height of the rectangular Pyramid = h
Volume of rectangular pyramid is the one-third of the base area times the height of pyramid.
Volume of rectangular pyramid = \(\frac{1}{3}\)Bh
Hence, the volume of the rectangular pyramid is \(\frac{1}{3}\)Bh

volume of the rectangular pyramid is \(\frac{1}{3}\)Bh.

Texas Go Math Volume of Rectangular Prism and Pyramid Answer Key Question 8.
Communicate Mathematical Ideas The prism and the pyramid in this activity have congruent bases and equal heights. Are they congruent three-dimensional shapes? Explain.
Answer:
The prism and pyramid cannot be considered as congruent three-dimensional shapes even if they have the same bases and equal heights. This is because their volumes are different. When a prism and pyramid have congruent bases and equal heights, the prism will have a greater volume than the pyramid. This is basically, the pyramid can fit inside the prism. The volume of the pyramid is only \(\frac{1}{3}\) of the volume of the prism.

No

Your Turn

Question 9.
Thé volume of a rectangular prism is 4\(\frac{1}{2}\) in³. What is the volume of a rectangular pyramid with a congruent base and the same height? Explain your reasoning.
Answer:
ragged right The volume of a rectangular prism is:
V = B . h (1)
The volume of a rectangular pyramid is:

They have congruent base and same height
Divide (1) by 3

The volume of a rectangular pyramid is three time less than the volume of a rectangular prism
The volume of a rectangular pyramid is:

The volume of a rectangular pyramid is three time less than the volume of a rectangular prism.
V_P = \(\frac{3}{2}\)in³

Solving Volume Problems

You can use the formulas for the volume of a rectangular prism and the volume of a rectangular pyramid to solve problems.

Volume of a Rectangular Pyramid
The volume V of a pyramid is one-third the area of its base B times its height h.
V = \(\frac{1}{3}\)Bh

Example 2
‘A Kyle needs to build a crate in the shape of a rectangular prism. The crate must have a volume of 38\(\frac{1}{2}\) cubic feet, and a base area of 15\(\frac{2}{3}\) square feet. Find the height of the crate.
V= Bh Use the formula.
38\(\frac{1}{2}\) = 15\(\frac{2}{5}\) . h Substitute for V and B.
\(\frac{77}{2}\) = \(\frac{77}{5}\)h Change the mixed numbers to fractions.
\(\frac{5}{77}\) . \(\frac{77}{2}\) = \(\frac{77}{5}\)h . \(\frac{5}{77}\) To divide both sides by \(\frac{77}{5}\), multiply both sides by the reciprocal.
\(\frac{5}{2}\) = h
The height of the crate must be \(\frac{5}{2}\) or 2\(\frac{1}{2}\), feet.

B. A glass paperweight in the shape of a rectangular pyramid has a base that is 4 inches by 3 inches and a height of 5 inches. Find the volume of the paperweight.
V= \(\frac{1}{3}\)Bh Use the formula.
V = \(\frac{1}{3}\) . 12 . 5 Think B = lw = 4 . 3 = 12
V = 20
The paperweight has a volume of 20 cubic inches.

Your Turn

Question 10.
A rectangular prism has a volume of 160 cubic centimeters and a height of 4 centimeters. What is the area of its base? _______
Answer:
V = B . h … (1)
V = 160 cm³ The volume of a prism
h = 4 cm Height of a prism
Divide (1) by h = 4

The area of the base is B = 40 cm².

Go Math Grade 7 Lesson 10.1 Answer Key Question 11.
A square pyramid has a base edge of 5.5 yards and a height of 3.25 yards. Find the volume of the pyramid to the nearest tenth. _______
Answer:
V = \(\frac{1}{3} B \cdot h\)
l = 5.5 yd Edge of base
h = 3.2 yd Height of pyramid
Find the base of a pyramid
B = (5.5). (5.5) = 30.25 yd²
Find the volume of a pyramid.
V = B . h = (30.25) . (3.25) = 98.3215 ≈ 98.3 yd³

The volume of a pyramid is V = 98.3 yd³.

Texas Go Math Grade 7 Lesson 10.1 Guided Practice Answer Key 

Question 1.
Find the volume of the rectangular prism. (Example 1)
V = Bh

Answer:
l = 6ft Length of base
w = 4\(\frac{1}{2}\) ft Width of a base
h = 9 ft Height of a prism
The volume of a prism:

V = 243 ft³

Identify the three-dimensional shape that can be formed from each net.
(Explore Activity 1 and Explore Activity 2)

Question 2.

Answer:
The three-dimensional shape that can be formed from the given net is Rectangular Pyramid. Because the in given
net all the four side have triangular shape and the base is of rectangular shape.

Question 3.

Answer:
The three-dimensional shape that can be formed from the given net is Pentagonal Prism. Because the in given net
all the four side and base have rectangular shape and front and behind of the prism is of pentagonal shape.
The three-dimensional shape that will be formed for the net ¡s also called as Heptahedron.

Question 4.

Answer:
The three-dimensional shape that can be formed from the given net is the Rectangular Prism. Because the in given net all the four sides have rectangular shapes and the base and top of the prism are square shapes.
The three-dimensional shape that will be formed for the net is also called a cuboid.

Go Math Lesson 10.1 Answer Key Volume of Mixed Pyramids Question 5.
The volume of a rectangular prism is 161.2 m³. The prism has a base that is 5.2 m by 3.1 m. Find the height of the prism. (Example 2)

Answer:
B = l . w Base of prism
l = 5.2 m Length of base
w = 3.1 m Width of base
h = ? Height of a prism
V = 161.2 m³ The volume of a prism
Use the formula B = l . w to find a base.
B = l . w = (5.2). (3.1) = 16.12 m²
Use the formula for the volume of a prism to find the height of the prism.
V = l . w . h

The height of the prism is h = 10 m.

Essential Question Check-In

Question 6.
Explain how to use models to show the relationship between the volume of a rectangular prism and a rectangular pyramid with congruent bases and heights.
Answer:
When you have a rectangular prism and rectangular pyramid with congruent bases and heights, you would notice that the rectangular pyramid can fit in the rectangular prism and there is still available space. This is because the prism will have a greater volume compared to the pyramid. Let’s say, that the rectangular prism will be filled with stones. The stones from the rectangular prism will be transferred to the rectangular pyramid notice that after the rectangular pyramid will be filled with stones and there are still remaining stones in the rectangular prism. This is because the volume of the rectangular pyramid is only \(\frac{1}{3}\) of the volume of the rectangular prism.

The relationship between a rectangular prism and rectangular pyramid with congruent bases and heights.

Texas Go Math Grade 7 Lesson 10.1 Independent Practice Answer Key  

Question 8.
Explain the Error A student found the volume of a rectangular pyramid with a base area of 92 square meters and a height of 54 meters to be 4,968 cubic meters. Explain and correct the error.
Answer:
Error in this conclusion is:
A student used formula for the volume of a prism (V = B . h), not for the volume of a pyramid (V_P = \(\frac{1}{3}\) . B. h).
That mistake can be corrected when the result divided with 3.
V = \(\frac{1}{3}\)B . h = \(\frac{1}{3}\) . 92 . 54 = \(\frac{1}{3}\) . 4968 = 1656

Error in this conclusion is:
A student used formula for the volume of a prism, not for the volume of a pyramid.
That mistake can be corrected when the result divided with 3.

Question 9.
A block of marble is in the shape of a rectangular prism. The block is 3 feet long, 2 feet wide, and 18 inches high. What is the volume of the block? _________________
Answer:
l = 3 ft Length of base
w = 2 ft Width of base
h = 1.5 ft Height of a prism
Use the formula B = l . w to find the base.
B = l . w = 3 . 2 = 6 ft²
Use the formula for the volume of a prism.
V = B . h
V = 6. (1.5)
V = 9 ft³

The volume of the block is V = 9 ft³.

Question 10.
Multistep Curtis builds a doghouse with base shaped like a cube and a roof shaped like a pyramid. The cube has an edge length of 3\(\frac{1}{2}\) feet.The height of the pyramid is 5 feet. Find the volume of the doghouse rounded to the nearest tenth.

Answer:
Base of doghouse is in the shape of a rectangular prism.
b = 3\(\frac{1}{2}\) = \(\frac{7}{2}\) ft Length of the base
h = \(\frac{7}{2}\)ft Height of a prism
Use the formula for the volume of a rectangular prism.
V₁ = b . b . h
= \(\frac{7}{2}\) . \(\frac{7}{2}\) . \(\frac{7}{2}\)
= \(\frac{343}{8}\) ft³
The roof of a doghouse is in the shape of rectangular pyramid.
b = \(\frac{7}{2}\) ft Length of the base
h = 5 ft Height of a pyramid
Use the formula for the volume of a rectangular pyramid.
V₂ = \(\frac{1}{3}\) . b . b . h
= \(\frac{1}{3}\) . \(\frac{7}{2}\) . \(\frac{7}{2}\) . 5
= \(\frac{245}{12}\) ft³
The volume of the doghouse is:
V = V₁ + V₂ = \(\frac{343}{8}\) . \(\frac{245}{12}\) = (42.875) + (20.416) ≈ 63.3 ft³
The Volume of the doghouse is V = 63.3 ft³

Question 11.
Miguel has an aquarium in the shape of a rectangular prism. The base is 30.25 inches long and 12.5 inches wide. The aquarium is 12.75 inches high. What is the volume of the aquarium to the nearest cubic inch?
Answer:
l = 30.25 in length of base
w = 12.5 in Width of base
h = 12.75 in Height of a prism
Use the formula B = l . w to find a base.
B = l . w = (30.25). (12.5) = 378.125 in²
Use the formula for the volume of a prism.
V = B . h.
= (378.125) . (12.75)
= 4, 821.09375 ≈ 4,821.09 in³

The volume of the aquarium is V = 4,821.09 in³.

Volume of Pyramid Answer Key Go Math Lesson 10.1 Question 12.
After a snowfall, Sheree built a snow pyramid. The pyramid had a square base with side lengths of 32 inches and a height of 28 inches. What was the volume of the pyramid to the nearest cubic inch?
Answer:
b = 32 in length of base
h = 28 in Height of a pyramid
Use the formula
B = b. b to find the base.
B = b . b = 32 . 32 = 1024 in²
Use the formula for the volume of a pyramid.
V = \(\frac{1}{3}\) . B . h
= \(\frac{1}{3}\) . 1024. 28
= \(\frac{1024.28}{3}\)
= 9, 557.333 ≈ 9, 557.3 in³

The volume of the pyramid is V = 9, 557.3 in³.

Question 13.
A storage chest has the shape of a rectangular prism with the dimensions shown. The volume of the storage chest is
18,432 cubic inches. What is its height?

Answer:
V = 18, 432 in³ The volume of the storage chest
l = 48 in Length of a base
w = 16m Width of a base
B = l . w = 48 . 16 = 768 m² Base area of a prism
The storage chest has the shape of a prism. Use the formula for the volume of a prism and substitute values for B and h.
V = B . h
18432 = 768 . h
Divide by 768 on both sides.
\(\frac{18432}{768}\) = h
24 = h

The height of the storage chest is 24 in.

Question 14.
Draw Conclusions A shipping company ships certain boxes at a special rate. The boxes must not have a volume greater than 2,500 cm³. Can the box shown be shipped at the special rate? Explain.

Answer:
Length of the given box = 10 cm
Width of the given box = 12 cm
H eight of the given box = 20 cm
We know that the volume of the box = Length × width × height
Volume of box = 10 × 12 × 20 cm³
= 2400 cm³
It is given in the problem that a shipping company ships certain boxes at a special rate only if the volume of the box is not greater than 2, 500 cm3 And the volume of the given box is 2, 400 cm³. So the box will be shipped at special rate by shipping company.
Yes, the box will be shipped at a special rate.

Yes, the box will be shipped at a special rate.

Question 15.
Communicate Mathematical Ideas Is the figure shown a prism or a pyramid? Justify your answer.

Answer:
Given figure is triangular Prism
Because prism is a figure which has parallel top and bottom bases. And pyramid has a base and triangular faces
which meet at common vertex point. In the given figure we can see that both triangle faces are parallel to each
other which has base length of 8 inch and height of 4 inch.

Question 16.
A cereal box can hold 144 cubic inches of cereal. Suppose the box is 8 inches long and 1.5 inches wide. How tall is the box?
Answer:
The cereal box is in the shape of rectangular prism.
l = 8 in Length of base
w = 1.5 in Width of base
h = ? Height of a prism
V = 144 in³ The volume of a prism
Use the formula B = l . w to find the base.
B = l . w = 8 . (1.5) = 12 in²
Use the formula for the volume of a prism to find the height of the prism.
V = B . h
144 = 12 . h
Divide both sides by 12.

The box is 12 in. tall.

Question 17.
A Shed in the shape of a rectangular prism has a volume of 1,080 cubic feet. The height of the shed is 8 feet, and the width of its base is 9 feet. What is the length of the shed?
Answer:
V = 1080 ft³ The volume of a rectangular prism
h = 8 ft Length of prism
l = ? Length of base
w = 9 ft Width of base
Use the formula for the volume of a prism to find a length of the base.
V = l . w . h.
1080 = l . 9 . 8
1080 = l . 72
Divide both sides by 72.

The length of shed is 15 ft.

H.O.T. Focus on Higher Order Thinking

Question 18.
Draw Conclusions Sue has a plastic paperweight shaped like a rectangular pyramid. The volume is 120 cubic inches, the height is 6 inches, and the length is 10 inches. She has a gift box that is a rectangular prism with a base that is 6 inches by 10 inches. How tall must the box be for it to hold the pyramid?
Answer:
Given volume of pyramid = 120 inch³
Height of pyramid = 6 inch
Length of pyramid = 10 inch
Volume of pyramid = \(\frac{\text { length } \times \text { width } \times \text { height }}{3}\)
120 = \(\frac{10 \times \text { width } \times 6}{3}\)
width = \(\frac{120 \times 3}{10 \times 6}\)
width = 6 inch
So, base of the pyramid is 6 inch by 10 inch and also the base of prism (box) is 6 inch by 10 inch. This means the height of pyramid to fit in completely but the volume of prism or box will be 3 times the volume of pyramid.
Hence, the box must be 6 inch tall to hold the pyramid.
This can be best understood by the given below figure in which pyramid is inside the prism with both having same base area.

Required height is 6 inch.

Question 19.
Represent Real-World Problems A public swimming pool is in the shape of a rectangular prism. The pool is 20 meters long and 16 meters wide. The pool is filled to a depth of 1.75 meters.
a. Find the volume of water in the pool.
h = 1.75 m Height of prism
l = 20 m Length of base
w = 16 m Width of base
Use the formula for the volume of a rectangular prism.
V = l . w . h
= 20 . 16 . (1.75)
= 320 . (1.75)
= 560 m³

The volume of water in the pool is 560 m³.

b. A cubic meter of water has a mass of 1,000 kilograms. Find the mass of the water in the pool.
Answer:
Mass of the water in the pool is:
560 . 1000 = 560,000 kg
The mass of the water in the pool is 560, 000 kg.

Question 20.
Analyze Relationships There are two glass pyramids at the Louvre Museum in Paris, France. The outdoor pyramid has a square base with side lengths of 35.4 meters and a height of 21.6 meters. The indoor pyramid has a square base with side lengths of 15.5 meters and a height of 7 meters. How many times as great is the volume of the outdoor pyramid than that of the indoor pyramid?
Answer:
The outdoor pyramid is in the shape of a rectangular pyramid.
b = 35.4 m Length of the base
h = 21.6 m Height of a pyramid
Use the formula for the volume of a rectangular pyramid.
V₁ = \(\frac{1}{3}\) . b . b . h
= \(\frac{1}{3}\)(35.4). (35.4). (21.6)
= 9,022.752 m³
The indoor pyramid is in the shape of a rectangular pyramid.
b = 15.5 m Length of the base
h = 7 m Height of a pyramid
Use the formula for the volume of a rectangular pyramid.
V₂ = \(\frac{1}{3}\) . b . b . h
= \(\frac{1}{3}\) . (15.5) . (15.5) . 7
= 560.583 m³
\(\frac{V_{1}}{V_{2}}\) = \(\frac{9022.752}{560.583}\) = 16.095 ≈ 16
The volume of the outdoor pyramid is 16 times greater then the volume of the indoor pyramid.

Question 21.
Persevere in Problem-Solving A small solid pyramid was installed on top of the Washington Monument in 1884. The square base of the pyramid is 13.9 centimeters on a side, and the height of the pyramid is 22.6 centimeters. The pyramid has a mass of 2.85 kilograms.

a. Find the volume of the pyramid. Round to the nearest hundredth.
Answer:
b = 13.9 cm length of the base
h = 22.6 cm Height of a pyramid
Use the formula for the volume of a rectangular pyramid
V₁ = \(\frac{1}{3}\) . b . b . h
= \(\frac{1}{3}\) . (13.9) . (13.9). (22.6)
= 1455.51 cm³
a. The volume of the pyramid is:
V = 1455.51 ≈ 1456 cm³

b. Find the mass of the pyramid in grams.
Answer:
The pyramid has mass of 285 kg. There are 1000 grams in 1 kilogram. Mass of the pyramid in grams is: 2.85 .
1000 = 2850 gr.

c. Science The density of a substance is the ratio of its mass to its volume. Find the density of the pyramid in grams per cubic centimeter. Round to the nearest hundredth.
Answer:
The density of the pyramid is \(\frac{\text { Mass }}{\text { Volume }}\) = \(\frac{2850}{1456}\) ≈ 2g/cm³.