Short Answer
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1.
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Billy used four kinds of toy prisms and a cylinder to build a house and a barn
as below right.
a. What are the volumes of the house
and the barn? b. What is the surface area of the
house? c. Given 1 in 3 = 2.54  2.54 
2.54 = 16.39 cm 3. What is the volume of a cube in cubic centimeters?
d. What is the volume of the house in cubic centimeters?
e. Given 1 in 2 =
2.54  2.54 = 6.45 cm 2. What is the surface area of a cube in square
centimeters? f. What is
the surface area of the house in square centimeters?
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2.
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One face of a cube has an area of 25 cm 2. a. What is the surface area of the
cube?
b. What is the volume of the cube?
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3.
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The bottom of a closed box has an area of 50 cm2. If the box is 8 cm
high, give at least three possibilities for the dimensions of the box.
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4.
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Each small cube in the rectangular prism below
has edges of length 2 cm.
a. What are the dimensions of the prism
in centimeters?
b. What
is the surface area of the prism in square centimeters?
c. How many 1-centimeter cubes would it
take to make a prism with the same dimensions as this prism? Explain your
reasoning.
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5.
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If you have N cubes, one arrangement that always forms a rectangular prism is 1
 1  N. For what values of N is this the only such
arrangement? Explain your thinking.
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6.
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Give the dimensions of three different rectangular prisms that have a volume of
240 cubic centimeters.
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7.
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The circumference of the base of a cylinder is 16 cm. The height of the cylinder
is 10 cm. a. What is the
surface area of the cylinder?
b. What is the volume of the
cylinder?
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8.
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The pictures below show the bases of three triangular prisms (not drawn to
scale). The height of the first prism is 80, and the volumes of all three prisms are the same. What
are the heights of the other two prisms?
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9.
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A tepee is a conical shaped tent used for shelter by the Plains Indians of North
America. Suppose a tepee has a radius of 9 ft and is 10 ft high. a. How much floor space does the tepee
have?
b. What is the
volume of the tepee?
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10.
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Find the volume of a sphere with a diameter of 100 cm.
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Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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11.
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Which pattern below correctly illustrates the surface area of a cylinder?
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12.
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What is the surface area of the can of soup?
 a. | 157.07 cm2 | b. | 628.32 cm2 | c. | 164.93
cm2 | d. | 282.74 cm2 |
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13.
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A cone has a base that is  cm 2 and a height of 10 cm.
What is the volume? a. | 125 cm3 | b. |  cm3 | c. | 
cm3 | d. |  cm3 |
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14.
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A rectangular prism has a volume of 154 in3. Which set of dimensions
below could be the dimensions of the prism?
a. | 6 by 8 by 3 | b. | 5 by 6 by 7 | c. | 2 by 7 by 11 | d. | 3 by 8 by
9 |
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15.
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Hillary is moving. She has many different boxes in which to pack her stuff. How
many times greater is the volume of the larger box compared to the volume of the smaller box?
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16.
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What is the approximate volume of a sphere with a diameter of 4
centimeters?
a. | 268 cm3 | b. | 134 cm3 | c. | 75 cm3 | d. | 33.5
cm3 |
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17.
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A box of cereal has a volume of 384 cubic inches. If the width of the box is 4
inches and the length is 8 inches, what is the height of the box?
a. | 6 in. | b. | 7 in. | c. | 12 in. | d. | 8
in. |
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18.
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A cylindrical pop can is 12.5 centimeters tall and 5.5 centimeters wide. What is
the volume of the pop can?
a. | 1187.91 cm3 | b. | 88.36 cm3 | c. | 215.98
cm3 | d. | 296.98 cm3 |
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19.
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Annie wanted to paint her living room walls blue. The room is 26 feet by 22 feet
by 8 feet high. How many cans of paint will she need if each gallon covers 88 square feet
(ignore doors and windows)?
a. | 6 cans | b. | 9 cans | c. | 8 cans | d. | 5
cans |
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20.
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Maurice’s family put a pool into their backyard. It is rectangular in
shape and its dimensions are 20 feet by 10 feet by 10 foot. It costs $0.05 per cubic ft to fill the
pool. How much will it cost Maurice’s family to fill their new pool?
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21.
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Find the perimeter of the rectangle with length 97 inches and width 17
inches.
a. | 228 in. | b. | 211 in. | c. | 1,649 in. | d. | 114
in. |
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22.
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Find the area of the rectangle with length 27 inches and width 40 inches.
a. | 67 in.2 | b. | 134 in.2 | c. | 1,080
in.2 | d. | 10,800 in.2 |
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23.
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A rectangular prism has a volume of 120 cm3. Its length is 5 cm and
its width is 8 cm. What is the prism’s height?
a. | 40 cm | b. | 3 cm | c. | 24 cm | d. | 15
cm |
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24.
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Maija is building a square sandbox with sides 2 feet long. She wants to put sand
1.55 feet deep in the box. How much sand should Maija order?
a. | 4 ft3 | b. | 1.55 ft3 | c. | 6.2 ft3 | d. | 3.1
ft3 |
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25.
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A driveway is 10 feet long, 15 feet wide, and 7 inches deep. How many cubic feet
of concrete will be required for the driveway? Round your answer to the nearest cubic foot, if
necessary.
a. | 150 ft3 | b. | 88 ft3 | c. | 70 ft3 | d. | 1050
ft3 |
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26.
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Name the solid according to its description:
The figure has one base that is
a rectangle and four lateral surfaces that are triangles.
a. | square pyramid | c. | rectangular prism | b. | cone | d. | rectangular
pyramid |
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Use a formula to find the surface area of the figure.
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27.
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When Tyson opens a cereal box and lays it out flat, he sees that both the top
and the bottom of the box measure 3 inches by 9 inches. Both sides of the box measure 3 inches by 12
inches, and both the front and back of the box measure 9 inches by 12 inches. What is the surface
area of the cereal box?
a. | 171 in. | b. | 342 in. | c. | 306 in. | d. | 234 in. |
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28.
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A construction crew is repairing a 201-ft-long section of a highway. The road is
8 ft wide, and the concrete must be poured to the depth of 6 in. How many cubic feet of concrete will
be required for the repair?
a. | 1,608 ft | b. | 804 ft | c. | 964.8 ft | d. | 9,648 ft |
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For the pair of similar solids, find the value of the variable.
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29.
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a. | 12 mm | b. |  mm | c. | 20 mm | d. | 
mm |
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30.
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A pyramid has a height of 5 in. and a surface area of 90 in.  .
Find the surface area of a similar pyramid with a height of 10 in. Round to the nearest tenth, if
necessary. a. | 360 in. | b. | 180 in. | c. | 22.5 in. | d. | 1.8 in. |
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31.
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A right cylinder has a radius of 6 m and a surface area of 84 m  . Find the surface area of a similar cylinder with a radius of 2 m. a. | 28 m | b. | 9.3 m | c. | 756 m | d. | 7 m |
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32.
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A rectangular prism has a width of 92 ft and a volume of 240 ft  . Find the volume of a similar prism with a width of 23 ft. Round to the nearest
tenth, if necessary. a. | 3.8 ft | b. | 60 ft | c. | 15 ft | d. | 10.4 ft |
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33.
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A cone has a radius of 15 cm and a volume of 540 cm  .
Find the volume of a similar cone with a radius of 10 cm. a. | 54 cm | b. | 240 cm | c. | 160 cm | d. | 360 cm |
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34.
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The ratio of corresponding dimensions of two similar solids is  . The
surface area of the first solid is 360 m  . Its volume is 360 m  . Find the surface area and volume of the second solid. Round each answer to the
nearest tenth, if necessary.
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35.
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Describe the base or bases of the figure. Name the part labeled  . Then name
the figure.  a. | circle; radius; cone | c. | circle; diameter; sphere | b. | circle; radius;
pyramid | d. | circle; diameter;
cylinder |
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Find the volume of the cone to the nearest cubic unit. Use a
calculator.
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36.
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a. | 1,810 in.3 | b. | 151 in.3 | c. | 452 in.3 | d. | 276
in.3 |
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37.
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height 8 cm; radius 15 cm
a. | 1,885 cm3 | b. | 1,461 cm3 | c. | 5,655 cm3 | d. | 22,619
cm3 |
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Find the volume of the square pyramid to the nearest cubic unit.
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38.
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a. | 175 m3 | b. | 233 m3 | c. | 58 m3 | d. | 88
m3 |
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39.
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edge 10 ft; height 11 ft
a. | 1,467 ft3 | b. | 550 ft3 | c. | 367 ft3 | d. | 1,100
ft3 |
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40.
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The diagram shows the dimensions of a teepee. Find the volume of the building to
the nearest cubic unit. Use 3.14 for p.  a. | 1,780 ft3 | b. | 1,382 ft3 | c. | 21,363
ft3 | d. | 5,341 ft3 |
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