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McGraw-Hill Math Grade 7 Unit Test Lessons 18–20 Answer Key
Question 1.
Armando is going to replace the trim around all of the doors in his house. The outside of each door measures 18 \(\frac{1}{2}\) feet. If he has 9 doors, how many inches of trim does he need to replace?
Answer:
1998 inches of trim.
Explanation:
18\(\frac{1}{2}\) convert in to inches
18 x 12 + \(\frac{1}{2}\) x 12
= 216 + 6
= 222
So, 222 x 9 = 1998 inches of trim.
Question 2.
Ashley wants to empty her fish tank before she cleans it. The fish tank holds 34 gallons. She is using a one-quart container to empty the tank by hand. How many full containers will she need to empty the tank?
Answer:
136 quarter containers need to empty the tank.
Explanation:
1 gallon = 4 quarters
The fish tank holds 34 gallons,
= 4 x 34 = 136 quarters
136 quarter containers need to empty the tank.
Question 3.
Annika weighed boxes for shipping books to customers. The first box weighed 160 ounces, the second box 3 weighed 10 \(\frac{3}{8}\) pounds, and the third box weighed \(\frac{1}{200}\) ton. Which box weighed the most?
Answer:
Second box weighed the most.
Explanation:
To compare the three boxes all should be of same units,
first convert the weights are in one unit pounds,
first box weighed 160 ounces = 10 pounds,
the second box 3 weighed 10 \(\frac{3}{8}\) pounds,
the third box weighed \(\frac{1}{200}\) ton = 1 pound,
Second box weighed the most.
Question 4.
Mandie wants to fence in her corral, and needs to know how much fencing to purchase. The corral has an irregular shape, with sides of 25 \(\frac{1}{4}\) feet, 330 inches, 6 yards, one foot, \(\frac{3}{160}\) of a mile, and 9 feet. How much fence material will she need?
________________ feet
Answer:
179.75 ft
Explanation:
All measures are converted in to one units as feet.
25 \(\frac{1}{4}\) feet = 25.25ft
330 inches = 27.5 ft
6 yards = 18 ft
one foot = 1
\(\frac{3}{160}\) of a mile = 99 ft
9 feet = 9 ft
25 \(\frac{1}{4}\) feet, 330 inches, 6 yards,
one foot, \(\frac{3}{160}\) of a mile, and 9 feet.
= 25.25 + 27.50 + 18 + 1 + 99 + 9
= 179.75 ft
Question 5.
What is the area of a rectangle with a length of 20 feet and a width of 144 inches?
_____________ square feet
Answer:
240 square feet.
Explanation:
144 in to be converted in to ft by dividing 12.
144/12 = 12 ft
the area of a rectangle = length x width.
A = l x w
A = 20 x 12
A = 240 sq ft
Question 6.
What is the area of a right triangle with sides of 6 feet, 8 feet, and 120 inches?
_____________ square feet
Answer:
24 sq ft.
Explanation:
120 in to be converted in to ft by dividing 12.
120/12 = 10 ft
the area of a triangle = (1/2) base x height,
A = (1/2) b x h
A = 0.5 x 6 x 8
A = 24 sq ft.
Question 7.
What is the volume of a rectangular box with sides of 48 inches and 3 \(\frac{1}{2}\) feet, and a height of 30 inches?
______________ cubic feet
Answer:
V = 35cu ft
Explanation:
To be converted in to ft by divide by 12.
30/12 = 2.5 ft
48/12 = 4 ft
Volume of a rectangular box V = l x b x h
V = 3.5 x 2.5 x 4
V = 35cu ft
Question 8.
A modern spacecraft must travel 8.1 miles per second in order to reach the planet Mars. How far does the spacecraft travel in a minute?
in an hour? ______________
in a day? ______________
Answer:
486 miles in a minute,
160 miles in an hour,
699,840 miles in a day.
Explanation:
8.1 miles per second.
1 minute = 60 seconds.
8.1 x 60 = 486 miles in a minute.
1 hour = 60 minutes.
486 x 60 = 29,160 miles in an hour.
1 day = 24 hours.
29,160 x 24 = 699,840 miles in a day.
Question 9.
If the distance to the moon from the earth is 248,000 miles, how long does it take the spacecraft in the previous exercise to travel to the moon? How many times a day could the spacecraft go back and forth between the moon and the earth?
Answer:
8.5 hours and 3 times.
Explanation:
The distance to the moon from the earth is 248,000 miles.
A modern spacecraft must travel 8.1 miles per second in order to reach the planet Mars,
486 x 60 = 29,160 miles in an hour.
248,000/29,160 = 8.5 hours.
8 x 3 = 24 hours.
Number of times in a day the spacecraft could go back and forth between the moon and the earth,
24 / 8.5 = 2.8 or 3 times.
Question 10.
The world record for the shot put is 23.12 meters. The world record for the discus throw is 74.08 meters. How many centimeters longer is the record for the discus throw than the record for the shot put?
Answer:
5096 cm
Explanation:
The shot put is 23.12 meters.
The discus throw is 74.08 meters.
Difference between disc throw and shot put,
74.08 – 23.12 = 50.96 meters.
1 meter = 100 cm.
50.96 x 100 = 5096 cm.
Question 11.
Stacey is measuring fabric for her grandmother, who is going to make a rectangular banner for the school. The banner will be 6.5 meters in length and 2,350 millimeters in width. How much fabric will Stacey’s grandmother need to buy?
______________ sq cm
Answer:
152,750sq cm
Explanation:
The banner will be 6.5 meters in length and 2,350 millimeters in width.
In the above given information, both units are of different to be converted to one unit.
Lets convert in to centimeters as below,
length = 6.5 meter x 100 cm = 650 cm
width = 2,350millimeters /10 = 235.0 cm
Area of a rectangle = Length x width
A = 650 x 235
A = 152,750 sq cm.
Question 12.
Sharon has three cans of latex paint to recycle. One can holds 2,957 milliliters of paint, the second can holds 105.6 centiliters of paint, and the third can holds 3.9 liters of paint. How much paint, in total, will Sharon be recycling?
______________ liters
Answer:
7.913 liters
Explanation:
In the given information all are of different units,
which are to be converted in to one unit as below to find out the total paint recycling.
One can holds 2,957 milliliters = 2.957 liters of paint,
the second can holds 105.6 centiliters =1.056 liters of paint,
and the third can holds 3.9 liters of paint.
paint, in total, will Sharon be recycling = 2.957 + 1.056 + 3.9
= 7.913 liters.
Question 13.
What is the area of a triangle with sides of 8 cm, 8 cm, a base of 4 cm, and a height of 6 cm?
_______________ sq cm
Answer:
12 sq cm
Explanation:
The area of a triangle with a base of 4 cm, and a height of 6 cm.
A = (1/2) x base x height
A = 0.5 x 4 x 6
A = 12 sq cm.
Question 14.
Jerrie walked around the entire rectangular school parking lot, which measures 106 meters by 7,500 centimeters. How far did Jerrie walk?
______________ meters
Answer:
Jerrie walks 362 meters.
Explanation:
In the given information all are of different units,
which are to be converted in to one unit as shown below.
Rectangular school parking lot, measures 106 meters long and 7,500 centimeters.
1 meter = 100 cm
7500 ÷ 100 =75 meters wide.
The perimeter of a rectangular park to be calculate as shown below.
P = 2(Length + Width)
P = 2 (106 + 75)
P = 2 (181)
P = 362 meters
So, Jerrie walks 362 meters.
Question 15.
How much topsoil can fit into a rectangular dump truck that measures 3.6 meters in width, 6.5 meters in length, and 3.5 meters high?
______________ cu meters
Answer:
81.9 cu meters.
Explanation:
The given information to find out the volume of the rectangular cuboid is,
3.6 meters in width, 6.5 meters in length, and 3.5 meters high.
Volume V = Length x Width x Height
V = 3.6 x 6.5 x 3.5
V = 81.9 cu meters
Question 16.
The average player on the soccer team measures 5 feet, 11 inches tall. About how tall is that in centimeters?
Answer:
180.34 cm
Explanation:
In the given information all are of different units,
which are to be converted in to one unit as shown below.
player on the soccer team measures 5 feet, 11 inches tall.
5 feet x 30 cm = 152.4 cm
11 inches x 2.5 = 27.94 cm
5 feet, 11 inches = 152.4 + 27.94
= 180.34 cm
Question 17.
The average taxicab has a gas tank that holds 85 liters of gasoline. How much is that in quarts?
______________ quarts
In gallons?
______________ quarts
Answer:
89.8 quarts;
22.45 gallons.
Explanation:
we know,
1 quart = 1.0567 liters
A gas tank holds 85 liters of gasoline.
85 x 1.0567 = 89.8 quarts,
1 gallon = 4 quarters = 3.7854 liters
85 /3.7854 = 22.45 gallons
Question 18.
Pauline measured a rectangular box and found that its dimensions were 55 inches by 32 inches by 20 inches tall. What is the total outside surface area in square inches?
_______________ sq in
In square feet? ______________ sq ft
Answer:
7000 sq in;
48.61 sq ft.
Explanation:
To find the surface area of a cuboid, add the areas of all 6 faces.
Dimensions were length 55 inches, width 32 inches and height 20 inches.
We can also label the length (l), width (w), and height (h) of the prism and use the formula as,
the surface area SA = 2lw + 2lh + 2hw
SA = 2 (55 x 32 + 32 x 20 + 20 x 55)
SA = 2 x (1760 + 640 +1100 )
SA = 2 x 3500
SA = 7000 sq in
To convert square in to sq foot by multiplying by 0.006944.
SA = 7000 sq in
SA = 7000 x 0.006944 = 48.61 sq ft.
Question 19.
A body temperature of 103.6° F is considered an extremely high fever. What temperature is that in Celsius?
Answer:
C = 39.7738° C
Explanation:
To convert temperatures in degrees Fahrenheit to Celsius,
subtract 32 and multiply by 0.5555 (or 5/9).
The notation C represents the temperature in Celsius, and F is the temperature in Fahrenheit.
C = 5/9 x (F – 32)
C = 0.5555 x (103.6 – 32)
C = 0.5555 x (71.6)
C = 39.7738° C
Question 20.
In track and field, the standard middle distance event is the 5,000 meters. About how many feet is 5,000 meters?
_____________ feet
Answer:
16,404 ft.
Explanation:
1 meter = 3.28 feet
5,000 meters = 5000 x 3.2808 ft
= 16,404 ft.
Question 21.
What is the volume of the rectangular pyramid?
Answer:
35 cu cm.
Explanation:
Area of rectangular base = length x width
B = 7 x 3 = 21 sq cm
volume of the rectangular pyramid = 1/3 x B x h
V = (1/3) x 21 x 5 = 35 cu cm.
Question 22.
What is the volume of the triangular solid?
Answer:
144 cubic in.
Explanation:
Volume of the triangular solid = Bh (Area of base x height)
B = Area of base = 1/2 bxh
B = 1/2 x 6 x 8 = 24 sq in
Volume V = Bh
V = 24 x 6
V = 144 cubic in
Question 23.
The air conditioning company suggests that people keep the temperature in their homes between 23 and 26 degrees Celsius during the summer. What is that range in degrees Fahrenheit?
Answer:
73.4 – 78.8 degrees Fahrenheit.
Explanation:
To convert temperatures in degrees Celsius to Fahrenheit,
add 32 and multiply by 1.8 (or 9/5).
The notation C represents the temperature in Celsius, and F is the temperature in Fahrenheit.
F = 9/5 x (C + 32)
If C = 23
F = 9/5 x (23 + 32)
F = \(\frac{9 X 23}{5}\) + 32
F = \(\frac{207}{5}\) + 32
F = 41.4 + 32
F = 73.4° F
If C = 26
F = 9/5 x (26 + 32)
F = \(\frac{9 X 26}{5}\) + 32
F = \(\frac{234}{5}\) + 32
F = 46.8 + 32
F = 78.8° F
Question 24.
The distance of a flight from Boston to Chicago is about 1,200 miles. The average ground speed for a commercial airliner is about 850 kilometers per hour. About how long will it take to fly from Boston to Chicago?
_______________ hours
Answer:
2\(\frac{1}{4}\)
Explanation:
Converting kilometers per hour in to miles per hour.
By multiplying the kilometer number with 0.62137 to get in miles.
850 x 0.62137 = 528.1645 miles per hour
Distance = Speed x Time
to calculate, how long will it take to fly from Boston to Chicago
Time = distance / speed
Time = 1200/528.1645 = 2.27 hours or 2\(\frac{1}{4}\) hours.