# Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume

### Guided Practice – Page No. 268

Find the circumference of each circle.

Question 1.

________ in

Explanation:
Circumference of the circle = 2πr = 2 x 22/7 x 9 = 56.57 in

Question 2.

________ cm

Explanation:
Circumference of the circle = 2πr = 2 x 22/7 x 7 = 44 cm

Find the circumference of each circle. Use 3.14 or $$\frac{22}{7}$$ for π. Round to the nearest hundredth, if necessary.

Question 3.
______ m

Question 4.

______ yd

Explanation:
Circumference of the circle = 2πr = 2 x 3.14 x 4.8 = 30.144 yd

Question 5.

______ in

Explanation:
Circumference of the circle = 2πr = 2 x 3.14 x 7.5 = 47.1 in

Question 6.
A round swimming pool has a circumference of 66 feet. Carlos wants to buy a rope to put across the diameter of the pool. The rope costs $0.45 per foot, and Carlos needs 4 feet more than the diameter of the pool. How much will Carlos pay for the rope?$ ______

Answer: $6.525 Explanation: Circumference of the swimming pool = 66 feet πd = 66 22/7 x d = 66 d = 66 x 7/ 22 = 10.5 The diameter of the pool = 10.5 feet Carlos needs 4 feet more than the diameter of the pool. Total rope needed = 10.5 + 4 = 14.5 feet Cost of rope per foot =$0.45
Total cost of the rope = 14.5 x $0.45 =$6.525
Therefore the total cost of the rope = $6.525 Find each missing measurement to the nearest hundredth. Use 3.14 for π. Question 7. r = d = C = π yd r = ________ yd d = ________ yd Answer: r = 0.5 yd d = 1 yd Explanation: Circumference = π yd 2πr = π yd r = 1/2 yd = 0.5 yd d = 2r = 2 [1/2] = 1 yd Question 8. r ≈ d ≈ C = 78.8 ft r ≈ ________ ft d ≈ ________ ft Answer: r = 495.31 ft d = 990.62 ft Explanation: Circumference = 78.8 ft 2πr = 78.8 ft r = 2 x 22/7 x 78.8 = 495.31 ft d = 2 x 495.31 = 990.62 ft Question 9. r ≈ d ≈ 3.4 in C = r ≈ ________ in C = ________ in Answer: r = 1.7 in c = 10.68 in Explanation: Diameter = 3.4 in Circumference = πd = 22/7 x 3.4 in = 10.68 in r = d/2 = 1.7 in Essential Question Check-In Question 10. Norah knows that the diameter of a circle is 13 meters. How would you tell her to find the circumference? Type below: ____________ Answer: Circumference = 16.82 meters Explanation: Given, Diameter = 13 meters Circumference = πd = 22/7 x 13 = 16.82 meters ### Independent Practice – Page No. 269 For 11–13, find the circumference of each circle. Use 3.14 or $$\frac{22}{7}$$ for π. Round to the nearest hundredth, if necessary. Question 11. _______ ft Answer: Cicumference = 18.526 ft = 19 ft (approx) Explanation: Given: Diameter = 5.9 ft Cicumference = πd = 3.14 x 5.9 = 18.526 ft = 19 ft (approx) Question 12. _______ cm Answer: Cicumference =176 cm Explanation: Given: Radius = 56 cm Cicumference = πd = 22/7 x 56 = 176 cm Question 13. _______ in Answer: Cicumference = 110 in Explanation: Given: Diameter = 35 in Cicumference = πd = 22/7 x 35 = 110 in Question 14. In Exercises 11–13, for which problems did you use $$\frac{22}{7}$$ for π? Explain your choice. Type below: _____________ Answer: 11th question as 3.14 and the 12 and 13 questions as π Explanation: We can take 3.14 as π for 11 th question because the diameter is given in decimal points. And in questions 12 and 13 we need to take π because the radius and diameter are given in whole number form. Question 15. A circular fountain has a radius of 9.4 feet. Find its diameter and circumference to the nearest tenth. d = _________ ft C = _________ ft Answer: d = 19 ft C = 59 ft Explanation: Given: Radius = 9.4 ft Diameter = 2r = 2 x 9.4 = 18.8 ft = 19 ft (approx) Circumference = πd = 22/7 x 18.8 = 59.08 = 59 ft (approx) Question 16. Find the radius and circumference of a CD with a diameter of 4.75 inches. r = _________ in C = _________ in Answer: r = 2.4 in C = 15 in Explanation: Given: Diameter = 4.75 in Radius = r/2 = 4.75/2 = 2.37 in = 2.4 in (approx) Circumference = πd = 22/7 x 4.75 = 14.92 in =15 in (approx) Question 17. A dartboard has a diameter of 18 inches. What are its radius and circumference? r = _________ in C = _________ in Answer: r = 9 in C = 56.6 in Explanation: Given: Diameter = 18 in Radius = r/2 = 18/2 = 9 in Circumference = πd = 22/7 x 18 = 56.57 in = 56.6 in (approx) Question 18. Multistep Randy’s circular garden has a radius of 1.5 feet. He wants to enclose the garden with edging that costs$0.75 per foot. About how much will the edging cost? Explain.
$_______ Answer: Explanation: Given: The radius of the garden= 1.5 ft Circumference of the garden = 2πr = 2 x 22/7 x 1.5 = 9.42 ft Cost of enclosing the garden per foot =$0.75
Total cost of edging = 9.42 x $0.75 =$7.06 = $7 (approx) Question 19. Represent Real-World Problems The Ferris wheel shown makes 12 revolutions per ride. How far would someone travel during one ride? _______ ft Answer: Total distance travelled in one ride is 4,752 ft Explanation: Given: The diameter of the Ferris wheel= 63 ft Circumference of the Ferris wheel = 2πr = 2 x 22/7 x 63 = 396 ft Total number of revolutions = 12 Total distance travelled = 12 x 396 = 4,752 ft Question 20. The diameter of a bicycle wheel is 2 feet. About how many revolutions does the wheel make to travel 2 kilometres? Explain. Hint: 1 km ≈ 3,280 ft _______ revolutions Answer: 1044 revolutions Explanation: Given: Diametre of the bicycle wheel = 2 feet Total distance travelled = 2 kilometres We know that, 1 km ≈ 3,280 ft 2 km = 2 x 3,280 = 6,560 ft Circumference of the bicycle = Distance travelled in one revolution = πd = 22/7 x 2 = 6.28 ft = 6.3 ft Total number of revolutions = Total distance travelled / distance travelled in one revolution = 6560 / 6.28 = 1044 revolutions Question 21. Multistep A map of a public park shows a circular pond. There is a bridge along a diameter of the pond that is 0.25 mi long. You walk across the bridge, while your friend walks halfway around the pond to meet you at the other side of the bridge. How much farther does your friend walk? _______ mi Answer: Explanation: Given, The diameter of the pond = 0.25 mi The length of the bridge = The diameter of the pond = 0.25 mi Then the distance walked by the man = 0.25 mi Distance travelled by the friend = Halfway around the pond to meet you at the other side of the bridge = πd/2 = 22/7 x 0.25/2 = 0.39 = 0.4 mi The friend travelled more distance compared to the man The more distance travelled by the friend = 0.39 – 0.25 = 0.14 mi ### Page No. 270 Question 22. Architecture The Capitol Rotunda connects the House and the Senate sides of the U.S. Capitol. Complete the table. Round your answers to the nearest foot. Type below: _____________ Answer: Radius = 48 ft Diameter = 96 ft Explanation: Given Height = 180 ft Circumference = 301.5 ft πd = 301.5 22/7 x d = 301.5 d = 95.93 = 96 ft r = d/2 = 96/2 = 48 ft H.O.T. Focus on Higher Order Thinking Question 23. Multistep A museum groundskeeper is creating a semicircular statuary garden with a diameter of 30 feet. There will be a fence around the garden. The fencing costs$9.25 per linear foot. About how much will the fencing cost altogether?
$_______ Answer: The total cost of fencing =$712

Explanation:
Given,
The diameter = 30 ft
Circumference of the garden in the shape of circle = 2πr
Circumference of the semicircle = πr = πd/2 =  22/7 x 30/2 = 47.14ft
Cost of fencing for each foot = $9.25 The total cost of fencing the semicircular garden = 47.14 x$9.25 + 30 x  $9.25 =$712 (approx)

Question 24.
Critical Thinking
Sam is placing rope lights around the edge of a circular patio with a diameter of 18 feet. The lights come in lengths of 54 inches. How many strands of lights does he need to surround the patio edge?
_______ strands

Answer: 12 and a half strands of light = 13 strands (approx)

Explanation:
Given,
The diameter of the circular patio = 18 ft = 216 inch
Circumference of the circular patio = πd = 22/7 x 216 = 678.85 inch
The lights will come in a length (in one strand)= 54 inches
Total number of strands of light required for the circular patio
= Circumference of the circular patio/ The lights will come in a length (in one strand) = 678.85/54 = 12.57 = 12 and a half strands of light

Question 25.
Represent Real-World Problems
A circular path 2 feet wide has an inner diameter of 150 feet. How much farther is it around the outer edge of the path than around the inner edge?
_______ feet

Explanation:
Given,
Width of the circular path = 2 ft
The inner diameter of the circular path = 150 ft
The outer diameter of the circular path = 150 + 2(2) = 154 ft
Inner circumference = πd = 150 π
Outer circumference =  πd = 154π
Distance between the outer and inner edge = 154 π – 150 π = 4 π = 12.6 ft

Question 26.
Critique Reasoning
Gear on a bicycle has the shape of a circle. One gear has a diameter of 4 inches, and a smaller one has a diameter of 2 inches. Justin says that the circumference of the larger gear is 2 inches more than the circumference of the smaller gear. Do you agree? Explain your answer.
_______

Justin statement is incorrect.

Explanation:
The circumference of the larger gear = πd = 4π
The circumference of the smaller gear = πd = 2π
Since, 2 x 2π = 4π, the circumference of the larger gear is two times the circumference of the smaller gear.
Since = 4π – 2π = 2π = 6.28
Therefore, The larger circumference is not 2 inches more than the smaller circumference

Question 27.
Persevere in Problem Solving
Consider two circular swimming pools. Pool A has a radius of 12 feet, and Pool B has a diameter of 7.5 meters. Which pool has a greater circumference? How much greater? Justify your answers.
_______

Explanation:
Given,
Pool A has a diameter = 24 ft
Pool B has a diameter = 7.5 m
We know that,
1 ft = 0.3 metres
24 ft = 7.2 metres
The pool B has a greater diameter so it has a greater circumference.
Circumference of the pool A = 7.2π
Circumference of the pool B = 7.5π
Difference between the circumferences = 7.5π – 7.2π = 0.9 meters.

### Guided Practice – Page No. 274

Find the area of each circle. Round to the nearest tenth if necessary. Use 3.14 for π.

Question 1.

_______ m2

Explanation:
Given:
Diameter = 14 m
Radius = 14/2 = 7 m
Area of the circle = πr2
= 3.14 x 7 x 7 = 153.86 = 153.9 m2

Question 2.

_______ mm2

Explanation:
Given:
Area of the circle = πr2
= 3.14 x 12 x 12 = 3.14(144) = 452.2mm2

Question 3.

_______ yd2

Explanation:
Given:
Diameter = 20yd
Area of the circle = πr2
= 3.14 x 10 x 10 = 3.14(100) = 314yd2

Solve. Use 3.14 for π.

Question 4.
A clock face has a radius of 8 inches. What is the area of the clock face? Round your answer to the nearest hundredth.
_______ in2

Explanation:
Given:
Area of the clock face = πr2
= 3.14 x 8 x 8= 3.14(64) = 200.96 in2

Question 5.
A DVD has a diameter of 12 centimeters. What is the area of the DVD? Round your answer to the nearest hundredth.
_______ cm2

Explanation:
Given:
Diameter = 12 centimeters
Radius = 12/2 = 6 centimeters
Area of the DVD= πr2
= 3.14 x 6 x 6 = 3.14(36) = 113.04 cm2

Question 6.
A company makes steel lids that have a diameter of 13 inches. What is the area of each lid? Round your answer to the nearest hundredth.
_______ in2

Explanation:
Given:
Diameter = 13 inches
Radius = 13/2 = 6.5 inches
Area of each lid= πr2
= 3.14 x 6.5 x 6.5 = 3.14(42.25) = 132.67 in2

Find the area of each circle. Give your answers in terms of π.

Question 7.
C = 4π
A =
Type below:
______________

Explanation:
Given:
Circumcenter = 4π
2πr = 4π
Radius = 4/2 = 2 units
Area of the circle = πr2
= π x 2 x 2 = π(4) = 4π square units

Question 8.
C = 12π
A =
Type below:
______________

Explanation:
Given:
Circumcenter = 12π
2πr = 12π
Area of the circle = πr2
= π x 6 x 6 = π(36) = 36π square units

Question 9.
C = $$\frac{π}{2}$$
A =
Type below:
______________

Explanation:
Given:
Circumcenter = $$\frac{π}{2}$$
2πr = $$\frac{π}{2}$$
Area of the circle = πr2
= π x 1/4 x 1/4 = π(1/16) = π/16 square units

Question 10.
A circular pen has an area of 64π square yards. What is the circumference of the pen? Give your answer in terms of π
Type below:
______________

Explanation:
Given:
Area of the circular pen = 64π square yards
πr2 = 64π
r = 8 yards
Circumference of the circle = 2πr = 2 x 8 x π = 16π yards

Essential Question Check-In

Question 11.
What is the formula for the area A of a circle in terms of the radius r?
Type below:
______________

Explanation:
Area of a circle = πr2

### Independent Practice – Page No. 275

Question 12.
The most popular pizza at Pavone’s Pizza is the 10-inch personal pizza with one topping. What is the area of a pizza with a diameter of 10 inches? Round your answer to the nearest hundredth.
_______ in2

Explanation:
Given:
Diameter = 10 inches
Radius = 10/2 = 5 inches
Area of a pizza = πr2
= 3.14 x 5 x 5 = 3.14(25) = 78.5 in2

Question 13.
A hubcap has a radius of 16 centimeters. What is the area of the hubcap? Round your answer to the nearest hundredth.

_______ cm2

Explanation:
Given:
Area of the circle = πr2
= 3.14 x 16 x 16 = 3.14(256) = 803.84 cm2

Question 14.
A stained glass window is shaped like a semicircle. The bottom edge of the window is 36 inches long. What is the area of the stained glass window? Round your answer to the nearest hundredth.
_______ in2

Explanation:
Area of the semicircle = 1/2 πr2 = 1/2(3.14)(18)(18) = 1/2 (3.14)(324) = 1.57(324) = 508.68 in 2

Question 15.
Analyze Relationships
The point (3,0) lies on a circle with the centre at the origin. What is the area of the circle to the nearest hundredth?
_______ units2

Explanation:
Area of the circle = πr2 = π(3)2 = 3.14(9) = 28.26 units2

Question 16.
Multistep
A radio station broadcasts a signal over an area with a radius of 50 miles. The station can relay the signal and broadcast over an area with a radius of 75 miles. How much greater is the area of the broadcast region when the signal is relayed? Round your answer to the nearest square mile.
_______ mi2

Explanation:
Given:
The greatest radius to which the broadcast can be relayed (R) = 75 miles
The greatest area of the broadcast region when the signal is relayed = πR2-πr2 = π(75) (75) – π (50) (50)
= 5625π – 2500π
= 3125π
= 3125(3.14) = 9813 mi2(approx)

Question 17.
Multistep
The sides of a square field are 12 meters. A sprinkler in the center of the field sprays a circular area with a diameter that corresponds to a side of the field. How much of the field is not reached by the sprinkler? Round your answer to the nearest hundredth.
_______ m2

Explanation:
Given:
The side of the square = 12 meters
The diameter circular area of the field in the centre = The side of the square = 12 meters
The radius of the field = 12/2 = 6 meters
Area of the field which is not reached by the sprinkler = Area of the square – Area of the circular area
= (side)2-πr2 = (12)(12) – π (6) (6)
= 144 – 36 (3.14)
= 144 – 113.04
= 30.96 m2

Question 18.
Justify Reasoning
A small silver dollar pancake served at a restaurant has a circumference of 2π inches. A regular pancake has a circumference of 4π inches. Is the area of the regular pancake twice the area of the silver dollar pancake? Explain.
_______

Answer: No, the area of the regular pancake is 4 times the area of the silver dollar pancake

Explanation:
Silver Dollar pancake:
Circumference of the silver Dollar pancake = 2π inches
2πr = 2π
r = 1 inch
Area of the silver dollar pancake = πr2 = π (1) (1) = π in2

Regular pancake:
Circumference of the regular pancake = 4π inches
2πr = 4π
r = 2 inch
Area of the silver dollar pancake = πr2 = π (2) (2) = 4π in2

Therefore, the area of the regular pancake is 4 times the area of the silver dollar pancake

Question 19.
Analyze Relationships
A bakery offers a small circular cake with a diameter of 8 inches. It also offers a large circular cake with a diameter of 24 inches. Does the top of the large cake have three times the area of that of the small cake? If not, how much greater is its area? Explain.
_______

Answer: No, the area of the large cake is 9 times the area of the small cake

Explanation:
Small Cake:
The diameter of the small cake= 8 inches
The radius of the small cake = 8/2 = 4 inches
Area of the small cake  = πr2 = π (4) (4) = 16 π in2

Large Cake:
The diameter of the large cake= 24 inches
The radius of the large cake = 24/2 = 12 inches
Area of the large cake  = πr2 = π (12) (12) = 144 π in2

Since 144 π/ 16 π = 9
Therefore the

area of the large cake is 9 times the area of the small cake.

### Page No. 276

Question 20.
Communicate Mathematical Ideas
You can use the formula A = $$\frac{C^{2}}{4π}$$ to find the area of a circle given the circumference. Describe another way to find the area of a circle when given the circumference.
Type below:
____________

Explanation:
Circumference of the circle = 2πr
C = 2πr
Divide both sides by 2π
then, r = C/2π
Area of the circle = πr2
Substitute C/2π for r:
Area = π(c/2π)2 = C2/4π

Question 21.
Draw Conclusions
Mark wants to order a pizza. Which is the better deal? Explain.

_____

Answer: The pizza of 18 inches is a better deal

Explanation:
Given:
The diameter of the pizza = 12 inches
The radius of the pizza = 12/2= 6 inches
Area of the circle = πr2
= (3.14)(6)(6) = 113 (approx) in2
The total cost of the pizza = $10 Cost of the pizza per inch =$10/113 = $0.09 per square inch The diameter of the pizza = 18 inches The radius of the pizza = 18/2= 9 inches Area of the circle = πr2 = (3.14)(9)(9) = 254 (approx) in2 The total cost of the pizza =$20
Cost of the pizza per inch = $20/254 =$0.08 per inch

Question 22.
Multistep
A bear was seen near a campground. Searchers were dispatched to the region to find the bear.
a. Assume the bear can walk in any direction at a rate of 2 miles per hour. Suppose the bear was last seen 4 hours ago. How large an area must the searchers cover? Use 3.14 for π. Round your answer to the nearest square mile.
_____ mi2

Explanation:
The bear can walk a distance = 2 x 4 = 8 miles
Since it is walking 2 miles per hour for 4 hours
The radius of the bear = 8 miles
Area of the circle = πr2
= (3.14)(8)(8) = 201 (approx) mi2

Question 22.
b. What If? How much additional area would the searchers have to cover if the bear were last seen 5 hours ago?
_____ mi2

Explanation:
If the bear for 5 hours then,
The bear can walk a distance = 2 x 5 = 10 miles
Since it is walking 2 miles per hour for 5 hours
The radius of the bear = 10 miles
Area of the circle = πr2
= (3.14)(10)(10) = 314 (approx) mi2

The additional area covered by the searches = 314 – 201 = 113 mi2

H.O.T.

Focus on Higher Order Thinking

Question 23.
Analyze Relationships
Two circles have the same radius. Is the combined area of the two circles the same as the area of a circle with twice the radius? Explain.
_____

Explanation:
If the radius of two circles is the same.
then, Let the radii of the circles be 1.
The area of each circle =  π square units
The combined area of 2 circles =π+π = 2π square units

then, Let the radii of the circles be 2
The area of each circle =  4π square units
The combined area of 2 circles =  4π+4π = 8π square units

Therefore the areas of both cases are not the same.

Question 24.
Look for a Pattern
How does the area of a circle change if the radius is multiplied by a factor of n, where n is a whole number?
Type below:
____________

Answer: The new area is then n2 times the area of the original circle.

Explanation:
If the radius is multiplied by a factor “n”
then, the new radius = rn
The area of the circle (with radius rn) = π(rn)= n2 (πr2).
Therefore the new area is n2 times the area of the original circle.

Question 25.
Represent Real World Problems
The bull’s-eye on a target has a diameter of 3 inches. The whole target has a diameter of 15 inches. What part of the whole target is the bull’s-eye? Explain.
Type below:
____________

Explanation:
Bull’s eye:
Diameter of Bull’s eye = 3 inches
Radius of Bull’s eye = 3/2 = 1.5 inches
Area of the Bull’s eye = π(r)= π(1.5)2 = 2.25π
Target:
Diameter of the target = 15 inches
Radius of the target = 15/2 = 7.5 inches
Area of the target = π(r)= π(7.5)2 = 56.25π

The part of Bull’s eye in the whole target = 2.25π/ 56.25π = 1/25

Therefore the 1/25th part of the whole target is the Bull’s eye.

### Guided Practice – Page No. 280

Question 1.
A tile installer plots an irregular shape on grid paper. Each square on the grid represents 1 square centimeter. What is the area of the irregular shape?

_____ cm2

Answer: Area of the irregular shape = 34 cm2

Explanation:
STEP1 First divide the irregular shapes into polygons.
STEP2 The irregular shape can be divided into a triangle, rectangle, parallelogram
STEP3 Areas of the polygons
Area of triangle = 1/2 (base x height) = 1/2 (4 x 2) = 4 cm2
Area of the rectangle = length x breadth = 5 x 3 = 15 cm2
Area of the parallelogram = base x height = 5 x 3 = 15 cm2
Area of the irregular shape = (15+15+5) cm2= 34cm2

Question 2.
Show two different ways to divide the composite figure. Find the area both ways. Show your work below.

_____ cm2

Answer: Area of the figure in both ways = 288 cm2

Explanation:
The first way to divide up the composite shape is to divide it into an 8 by 9 rectangle and a 12 by 18 rectangle.
The area of the first rectangle = Length x breadth = 9 x 8 = 72 cm2
The area of the second rectangle =  Length x breadth = 18 x 12 = 216 cm2
The total area of the figure = 72 + 216 = 288 cm2

Question 3.
Sal is tiling his entryway. The floor plan is drawn on a unit grid. Each unit length represents 1 foot. Tile costs $2.25 per square foot. How much will Sal pay to tile his entryway?$ _____

Answer: Sal will pay $97.875 Explanation: Separate this figure into trapezium and parallelogram. Area of the trapezium = 1/2 (a+b)h = 1/2 (7+4) 5 = 1/2 (11) 5 = 27.5 ft2 Area of the parallelogram = base x height = 4 x 4 = 16 ft2 The total area of the figure = 27.5 + 16 = 43.5ft2 Cost of each square foot =$2.25
Amount paid by Sal = 43.5 x 2.25 = $97.875 Essential Question Check-In Question 4. What is the first step in finding the area of a composite figure? Type below: ______________ Answer: The first step in finding the area of a composite figure is to divide it up into smaller basic shapes. Explanation: The first step in finding the area of a composite figure is to divide it up into smaller basic shapes such as triangles, squares, rectangles, parallelograms, circles and trapezium. Then calculate the area of each figure and add them to find the area of the figure. ### Independent Practice – Page No. 281 Question 5. A banner is made of a square and a semicircle. The square has side lengths of 26 inches. One side of the square is also the diameter of the semicircle. What is the total area of the banner? Use 3.14 for π. _____ in2 Answer: 941.33 in2 Explanation: Area of the square = side x side = 26 x 26 = 676 in2 Area of the semicircle =1/2 πr2= 1/2 (3.14) (13) (13) = 1/2 (3.14) (169) = 265.33 in2 Area of the figure = 676 + 265.33 = 941.33 in2 Question 6. Multistep Erin wants to carpet the floor of her closet. A floor plan of the closet is shown. a. How much carpet does Erin need? _____ ft2 Answer: 61 ft2 Explanation: Area of the rectangle = length x breadth = 4 x 10 = 40 ft Area of the triangle = 1/2 x base x height = 1/2 x 6 x 7 = 21 ft The total area of the figure = 40+21 = 61 ft2 Question 6. b. The carpet Erin has chosen costs$2.50 per square foot. How much will it cost her to carpet the floor?
$_____ Answer:$152.50

Explanation:
Cost per square foot of the carpet = $2.50 The total cost of the carpet on the floor = 61 x$2.50 =$152.50 Question 7. Multiple Representations Hexagon ABCDEF has vertices A(-2, 4), B(0, 4), C(2, 1), D(5, 1), E(5, -2), and F(-2, -2). Sketch the figure on a coordinate plane. What is the area of the hexagon? _____ units2 Answer: The area of the figure is 30 square units Explanation: Separate the figure into a trapezium and a rectangle. Area of a trapezium = 1/2 (a+b) h= 1/2 (2+4) x 3 = 1/2 (6) 3 = 9 square units Area of a rectangle = length x breadth = 7 x 3 = 21 square units The total area of the figure = 9+21 = 30 square units Question 8. A field is shaped like the figure shown. What is the area of the field? Use 3.14 for π. _____ m2 Answer: 146.24 m2 Explanation: Divide the figure into a square, triangle and a quarter of a circle. Area of a square = side x side = 8 x 8 = 64 m2 Area of a quarter of a circle = 1/4 (πr2) = 1/4 (3.14 x 82) = 1/4 (200.96) = 50.24 m2 Area of the triangle = 1/2 x base x height = 1/2 x 8 x 8 = 32 m2 Total area of the figure = 64+32+50.24 = 146.24 m2 Question 9. A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 12 cm long and 4 cm wide. The diameter of each semicircle is the width of the rectangle. What is the area of the bookmark? Use 3.14 for π. _____ cm2 Answer: 60.56 cm2 Explanation: The bookmark is divided into a rectangle, semicircle. Area of the rectangle = length x breadth = 12 x 4 = 48 cm2 The diameter of the semicircle = The width of the rectangle = 4 cm The radius of the semicircle = 4/2 = 2 cm The area of the semicircle = πr2 = 3.14 x 2 x 2 = 12.56 cm2 The total area of the bookmark = 12.56 + 48 = 60.56 cm2 Question 10. Multistep Alex is making 12 pendants for the school fair. The pattern he is using to make the pennants is shown in the figure. The fabric for the pennants costs$1.25 per square foot. How much will it cost Alex to make 12 pennants?

$_____ Answer:$52.50

Explanation:
Each pendant is made up of a rectangle and a triangle.
Area of the rectangle = length x breadth = 3 x 1 = 3 ft2
Area of the triangle = 1/2 x base x height = 1/2 x 1 x 1 = 0.5 ft2
The total area of the pendant = 3+0.5 = 3.5 ft2
Number of pendants = 12
Area of the pendants = 12 x 3.5 = 42 ft2
Total cost = $480 then, 12x + 150 = 480 Question 5. What is the volume of the prism? Options: a. 192 ft3 b. 48 ft3 c. 69 ft3 d. 96 ft3 Answer: d. 96 ft3 Explanation: B = Base area of the triangle = 1/2 x 8 x 2 = 8 ft2 Height = 12 ft Volume of the triangular orism = Bh = 8(12) = 96 ft3 Question 6. A school snack bar sells a mix of granola and raisins. The mix includes 2 pounds of granola for every 3 pounds of raisins. How many pounds of granola are needed for a mix that includes 24 pounds of raisins? Options: a. 16 pounds b. 36 pounds c. 48 pounds d. 120 pounds e. 120 pounds Answer: a. 16 pounds Explanation: 2/3 is equal to x/24 then 3 times 8 is equal to 24 and if 2 times 8 is equal to 16. Question 7. Find the percent change from$20 to $25. Options: a. 25% decrease b. 25% increase c. 20% decrease d. 20% increase Answer: b. 25% increase Explanation: 25 – 20 = 5 divide by 20 = 1/4 When we find the percentage we get 25. So we can say that there is an increase in 25% Question 8. Each dimension of the smaller prism is half the corresponding dimension of the larger prism. a. What is the surface area of the figure? _____ in2 Answer: 856 in2 Explanation: Height of the top prism = 10/2 = 5 Length of the top prism = 16/2 = 8 Width of the top prism = 8/2 = 4 Perimeter = 2l + 2w = 2(8) + 2(4) = 16 + 8 = 24 in B = lw = 8(4) = 32 in Surface area of top prism= Ph + 2B = 24(5) + 2(32) = 184 in2 Height of the prism = 10 Length of the prism = 16 Width of the prism = 8 Perimeter = 2l + 2w = 2(16) + 2(8) = 32 + 16 = 48 in B = lw = 16(8) = 128 in Surface area of bottom prism= Ph + 2B = 48(10) + 2(128) = 736 in2 Area of overlapping region = 32 in2 The total surface area of the prism = Surface area of top prism + Surface area of bottom prism – 2[Area of overlapping region ] = 184 + 736 – 2(32) = 856 in2 Question 8. b. What is the volume of the figure? _____ in3 Answer: 1440 in3 Explanation: Volume of top prism = Bh = 32(5) = 160 in3 Volume of bottom prism = Bh = 128(10) = 1280 in3 The total volume of the figure = 160 + 1280 = 1440 in3 ### EXERCISES – Page No. 298 Question 1. In the scale drawing of a park, the scale is 1 cm: 10 m. Find the area of the actual park. _____ m2 Answer: 450 m2 Explanation: Multiply the dimensions of the scale drawing by 10 since 1 cm = 10 m 3cm by 1.5 cm = 30m by 15 m Area = 30(15) = 450 m2 Question 2. Find the value of y and the measure of ∠YPS. y = __________ ° mYPS = __________ ° Answer: y = 8 mYPS = 40 ° Explanation: 140 + 5y = 180 [sum of angle on a line = 180°] 5y = 40 y = 8 mYPS = mRPZ = 5y [vertically opposite angles] mYPS = 5(8) = 40° Question 3. Kanye wants to make a triangular flower bed using logs with the lengths shown below to form the border. Can Kanye form a triangle with the logs without cutting any of them? Explain. _____ Answer: No Explanation: A side of a triangle must be greater than the difference of the other two sides and smaller than the sum of the other 2 sides. The sum of the first 2 sides = 3+4 = 7 < 8 Therefore, he cannot form a triangle unless he cuts the logs. Question 4. In shop class, Adriana makes a pyramid with a 4-inch square base and a height of 6 inches. She then cuts the pyramid vertically in half as shown. What is the area of each cut surface? _____ in2 Answer: 12 in2 Explanation: Base = 4 in Height = 6 in Area of the triangle = 1/2 x 6 x 4 = 12 in2 ### Page No. 300 Find the circumference and area of each circle. Round to the nearest hundredth. Question 1. C = __________ in A = __________ in2 Answer: C = 69.08 in A = 379.94 in2 Explanation: Diameter = 22 in Radius = d/2 = 22/2 = 11 in C = 2 πr = 2 π(11) = 22 (3.14) = 69.08 in A = πr2 = 3.14 (11)2 = 379.94 in2 Question 2. C = __________ m A = __________ m2 Answer: C = 28.26 m A = 63.59m2 Explanation: Radius = 4.5 m C = 2 πr = 2 π(4.5) = 9 (3.14) = 28.26 m A = πr2 = 3.14 (4.5)2 = 63.59 m2 Find the area of each composite figure. Round to the nearest hundredth if necessary. Question 3. ______ in2 Answer: 99 in2 Explanation: Area of the square = 9 x 9 = 81 in2 Base of the triangle = 13 – 9 = 4 in Area of the triangle = 1/2 x 4 x 9 = 18 in2 The total area of the figure = 81 + 18 = 99 in2 Question 4. ______ cm2 Answer: 420.48 cm2 Explanation: Area of the rectangle = 16 x 20 = 320 cm2 Diameter = 16 cm Radius = 16/2 = 8 cm Area of the semi circle = 1/2 πr2 = 1/2 x 3.14 (8)2 = 100.48 cm2 The total area of the figure = 320 + 100.48 = 420.48 cm2 Find the volume of each figure. Question 5. ______ in3 Answer: 420 in3 Explanation: B = 7(5) = 35 in2 V = Bh = 35 x 12 = 420 in3 Question 6. The volume of a triangular prism is 264 cubic feet. The area of a base of the prism is 48 square feet. Find the height of the prism. ______ in Answer: 5.5 ft Explanation: V = Bh 264 = 48h h = 264/48 = 5.5ft ### Page No. 301 A glass paperweight has a composite shape: a square pyramid fitting exactly on top of an 8 centimeter cube. The pyramid has a height of 3 cm. Each triangular face has a height of 5 centimeters. Question 7. What is the volume of the paperweight? ______ cm3 Answer: 576 cm3 Explanation: Pyramid: B = 8 x 8 = 64 cm2 V = 1/3 Bh = 1/3 x 64 x 3 = 64 cm3 Prism: B = 8 x 8 = 64 cm2 V = Bh = 64 x 8 = 512 cm3 The total volume of the figure = 64 + 512 = 576 cm3 Question 8. What is the total surface area of the paperweight? ______ cm2 Answer: 400 cm2 Explanation: Pyramid: P = 4(8) = 32 cm S = 1/2 Pl + B = 80 + 64 = 144 cm2 Prism: P = 4(8) = 32 cm S = Ph + 2B = 32(8) + 2(64) = 384 cm2 The total surface area of the prism = Area of the prism + Area of the pyramid – 2[Area of the overlapping region] = 144 + 384 – 2(64) = 400 Unit 4 Performance Tasks Question 9. 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. How many square feet of material does Miranda need to make the tent (including the floor)? Show your work. ______ ft2 Answer: 261 3/4 ft2 Explanation: P = 2 x 7 1/2 + 8 = 22 1/2 B = 4/2 (8) (6) = 24 S = Ph + 2B = 22 1/2 x 9 1/2 + 2(24) = 213 3/4 + 48 = 261 3/4 ft2 Question 9. b. What is the volume of the tent? Show your work. ______ ft3 Answer: 228 ft3 Explanation: V = Bh = 24 x 9 1/2 = 228 ft3 Question 9. c. 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 Type below: ____________ Answer: Increase the height to 10.45 ft Explanation: New volume = 1.10 x 228 = 250.8 250.8 = 24h h = 10.45 ft ### Unit 4 Performance Tasks (cont’d) – Page No. 302 Question 10. 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. ______ cm3 Answer: 135,000 cm3 Explanation: B = 45 x 25 = 1125 cm2 V = Bh = 1125 x 120 = 135,000 cm3 Question 10. 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. ______ cm3 Answer: 116,702 cm3 Explanation: Width = 45 – 2(1) = 43 ft Length = 25 – 2(1) =23ft Height = 120-2(1) = 118ft B = 43 x 23 = 989 ft2 V = Bh = 989 x 118 = 116,702 ft3 ### Selected Response – Page No. 303 Question 1. A school flag is in the shape of a rectangle with a triangle removed as shown. What is the measure of angle x? Options: a. 50° b. 80° c. 90° d. 100° Answer: d. 100° Explanation: x = 50 + 50 = 100° [ Sum of two angles created by the 2 lines] Question 2. On a map with a scale of 2 cm = 1 km, the distance from Beau’s house to the beach is 4.6 centimetres. What is the actual distance? Options: a. 2.3 km b. 4.6 km c. 6.5 km d. 9.2 km Answer: a. 2.3 km Explanation: 2/1 = 4.6/x x = 4.6/2 = 2.3 km Question 3. Lalasa and Yasmin are designing a triangular banner to hang in the school gymnasium. They first draw the design on paper. The triangle has a base of 5 inches and a height of 7 inches. If 1 inch on the drawing is equivalent to 1.5 feet on the actual banner, what will the area of the actual banner be? Options: a. 17.5 ft2 b. 52.5 ft2 c. 39.375 ft2 d. 78.75 ft2 Answer: c. 39.375 ft2 Explanation: 1in = 1.5ft The base of the triangle = 5 in = 1.5(5) ft = 7.5 ft Height = 7 in = 7(1.5) ft = 10.5 ft Area of the triangle = 1/2 x 7.5 x 10.5 = 39.375 ft2 Question 4. Sonya has four straws of different lengths: 2 cm, 8 cm, 14 cm, and 16 cm. How many triangles can she make using the straws? Options: a. no triangle b. one triangle c. two triangles d. more than two triangles Answer: b. one triangle Explanation: The third side of a triangle must be smaller than the sum of the other two sides to form a triangle. 2+8 = 10<14 2+8 = 10<16 8+14 = 22>14 8+14 = 22>16 2+14 = 16=16 2+16 = 18>16 Therefore, only one triangle can be formed using the sides 8, 14, 16. Question 5. 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?
Options:
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:
If x is the number of additional toppings, then 1.25 x is the cost of the additional toppings.
This gives the total cost is 1.25x + 15
then,
1.25x + 15 = 20

Question 6.
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? Options: a.$15680
b. $17360 c.$19040
d. $20720 Answer: c.$19040

Explanation:
Simple interest = 14,000 x 0.12 x 2 = $5,040 Amount =$14,000 + $5,040 =$19040

Question 7.
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?
Options:
a. 2.5 cm3
b. 750 cm3
c. 1125 cm3
d. 2250 cm3

Explanation:
V = Bh = 30(75) = 2250cm3

Question 8.
Consider the right circular cone shown.

If a vertical plane slices through the cone to create two identical half cones, what is the shape of the cross section?
Options:
a. a rectangle
b. a square
c. a triangle
d. a circle

Explanation:
Slicing through the vertex to create 2 identical half cones would create a cross-section that  is a triangle.

### Page No. 304

Question 9.
The radius of the circle is given in meters. What is the circumference of the circle? Use 3.14 for π.

a. 25.12 m
b. 50.24 m
c. 200.96 m
d. 803.84 m

Explanation:
Circumference = 2 πr = 2 π(8) = 16 (3.14) = 50.24 m

Question 10.
The dimensions of the figure are given in millimeters. What is the area of the two-dimensional figure?

Options:
a. 39 mm2
b. 169 mm2
c. 208 mm2
d. 247 mm2

Explanation:
Area of the square = 13 x 13 = 169 mm2
Area of the triangle = 1/2 x 13 x 6 = 39 mm2
The total area of the figure = 169 + 39 = 208 mm2

Question 11.
A forest ranger wants to determine the radius of the trunk of a tree. She measures the circumference to be 8.6 feet. What is the trunk’s radius to the nearest tenth of a foot?
Options:
a. 1.4 ft
b. 2.7 ft
c. 4.3 ft
d. 17.2 ft

Explanation:
Circumference = 2 πr = 8.6 ft
r = 8.6/2 π = 1.4 ft

Question 12.
What is the measure in degrees of an angle that is supplementary to a 74° angle?
Options:
a. 16°
b. 74°
c. 90°
d. 106°

Explanation:
Sum of supplementary angles = 180°
x + 74° = 180°
x = 106°

Question 13.
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?
Options:
a. 19.7 cm3
b. 108.5 cm3
c. 217 cm3
d. 237.4 cm3

Explanation:
V = Bh
B = 6.2 x 3.5 = 21.7 cm2
h = 10 cm
V = 21.7 x 10 = 217 cm3

Question 14.
A patio is the shape of a circle with diameter shown.

What is the area of the patio? Use 3.14 for π.
Options:
a. 9 m2
b. 28.26 m2
c. 254.34 m2
d. 1017.36 m2

Explanation:
Diameter = 18 m
Radius = 18/2 = 9 m
Area of the patio = πr2 = 3.14 (9)2 = 254.34 m2

Question 15.
Petra fills a small cardboard box with sand. The dimensions of the box are 3 inches by 4 inches by 2 inches.
a. What is the volume of the box?
______ in3

Explanation:
V = Bh
B = 3 x 4 = 12 in2
V = 12 x 2 = 24 in3

Question 15.
b. Petra decides to cover the box by gluing on wrapping paper. How much wrapping paper does she need to cover all six sides of the box?
______ in2

Explanation:
P = 2(3) + 2(4) = 6 + 8 = 14 in
S = Ph + 2B = 14 x 2 + 2 x 24 = 76 in2

Question 15.
c. Petra has a second, larger box that is 6 inches by 8 inches by 4 inches. How many times larger is the volume of this second box? The surface area?
Volume is _________ times greater.
Surface area is _________ times greater