Geometry

Cindy J. Boyd, Jerry Cummins, Carol E. Malloy

Chapter 13

Extending Volume - all with Video Answers

Educators

Section 1

Volumes of Prisms and Cylinders

Problem 1

Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Ethan Somes

Numerade Educator

Problem 2

Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 3

Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 4

The world's most powerful digital camera is located in New Mexico at the Apache Point Observatory. It is surrounded by a rectangular prism made of aluminum that protects the camera from wind and unwanted light. If the prism is 12 feet long, 12 feet wide, and 14 feet high, find its volume to the nearest cubic foot.

Ethan Somes

Numerade Educator

Problem 5

Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 6

Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 7

Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 8

Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 9

Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 10

Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 11

Find the volume of each oblique prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 12

Find the volume of each oblique prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 13

Find the volume of each oblique prism or cylinder. Round to the nearest tenth if necessary.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 14

The volume of a cylinder is 615.8 cubic meters, and the height is 4 meters. Find the length of the diameter of the cylinder.

Ethan Somes

Numerade Educator

Problem 15

The volume of a rectangular prism is 1152 cubic inches, and the area of the base is 64 square inches. Find the length of the lateral edge of the prism.

Ethan Somes

Numerade Educator

Problem 16

Find the volume of the solid formed by each net. FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 17

Find the volume of the solid formed by each net. FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 18

Find the volume of the solid formed by each net. FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 19

The base of a rectangular swimming pool is sloped so one end of the pool is 6 feet deep and the other end is 3 feet deep. If the length of the pool is 20 feet and the width is 15 feet, find the volume of water it takes to fill the pool.

Ethan Somes

Numerade Educator

Problem 20

In a sandcastle competition, contestants are only allowed to use water, shovels, and 10 cubic yards of sand. In order to transport the correct amount of sand, they want to create cylinders that are 6 feet tall to hold enough sand for one contestant. What should the diameter of the cylinders be?

Ethan Somes

Numerade Educator

Problem 21

Find the volume of each solid to the nearest tenth. FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 22

Find the volume of each solid to the nearest tenth. FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 23

Manny is building a blanket chest for his sister. His design is a composite of a square prism and half of a cylinder. What is the volume of the hope chest? FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 24

The New England Aquarium in Boston, Massachusetts, has one of the world's largest cylindrical tanks. The Giant Ocean Tank holds approximately $200,000$ gallons and is 23 feet deep. If it takes about $7 \frac{1}{2}$ gallons of water to fill a cubic foot, what is the radius of the Giant Ocean Tank?

Ethan Somes

Numerade Educator

Problem 25

A can 12 centimeters tall fits into a rubberized cylindrical holder that is 11.5 centimeters tall, including 1 centimeter, which is the thickness of the base of the holder. The thickness of the rim of the holder is 1 centimeter. What is the volume of the rubberized material that makes up the holder?
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 26

A soy milk company is planning a promotion in which the volume of soy milk in each container will be increased by $25 \% .$ The company wants the base of the containers to stay the same. What will be the height of the new containers?
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 27

Mrs. Blackwell is planning to remove an old patio and install a new rectangular concrete patio 20 feet long, 12 feet wide, and 4 inches thick. One contractor bid $\$ 2225$ for the project. A second contractor bid $\$ 500$ per cubic yard for the new patio and $\$ 700$ for removal of the old patio. Which is the less expensive option? Explain.

Ethan Somes

Numerade Educator

Problem 28

Find a real prism or cylinder. Measure its dimensions and find its volume.

Ethan Somes

Numerade Educator

Problem 29

Find the volume of the resulting part

Ethan Somes

Numerade Educator

Problem 29

Machinists make parts for intricate pieces of equipment. Suppose a part has a regular hexagonal hole drilled in a brass block.
Find the volume of the resulting part.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 30

Machinists make parts for intricate pieces of equipment. Suppose a part has a regular hexagonal hole drilled in a brass block.
The density of a substance is its mass per unit volume. At room temperature, the density of brass is 8.0 grams per cubic centimeter. What is the mass of this block of brass?
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 31

Draw a prism that has a volume of 50 cubic centimeters.

Ethan Somes

Numerade Educator

Problem 32

Che and Julia are trying to find the volume of the oblique prism. Who is correct? Explain your reasoning. FIGURE CAN'T COPY.
Che $v=B h$ $=(12)(8)(6)$ $=576 \mathrm{cm}^{3}$
Julia $V=B h$ $=(12)(8)(4)$ $=384 \mathrm{cm}^{3}$

Kaci Long

Numerade Educator

Problem 33

Writing in Math Refer to the information on page 728 to explain how mathematics is sometimes used in comics. Differentiate between the mathematical meaning of volume and Shoe's meaning of volume.

Ethan Somes

Numerade Educator

Problem 33

A 40-story building is a rectangular prism with a length of 300 feet and a width of 220 feet. On top of the rectangular prism is a triangular prism the base of which has a height of 150 feet and a base of 220 feet. If each story is 11 feet, find the volume of the building. FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 34

What is the volume of a 3 -dimensional object with the dimensions shown in the three views below?
FIGURE CAN'T COPY.
A $59.1 \mathrm{cm}^{3}$
B $67.1 \mathrm{cm}^{3}$
C $68.4 \mathrm{cm}^{3}$
D $103.4 \mathrm{cm}^{3}$

Ethan Somes

Numerade Educator

Problem 34

Refer to the information on page 728 to explain how mathematics is sometimes used in comics. Differentiate between the mathematical meaning of volume and Shoe's meaning of volume.

Ethan Somes

Numerade Educator

Problem 35

What is the volume of a 3 -dimensional object with the dimensions shown in the three views below?
A $59.1 \mathrm{~cm}^{3}$
B $67.1 \mathrm{~cm}^{3}$
C $68.4 \mathrm{~cm}^{3}$
D $103.4 \mathrm{~cm}^{3}$

Ethan Somes

Numerade Educator

Problem 36

Every person on a basketball team gets one paper cup for water during each practice. The table shows the number of paper cups remaining $c$ after each practice $p.$
$$\begin{array}{|c|c|}
\hline \text { Number of Practices } & \text { Cups Left } \\
\hline 1 & 262 \\
\hline 2 & 244 \\
\hline 3 & 226 \\
\hline 4 & 208 \\
\hline 5 & 190 \\
\hline
\end{array}$$
Which function can be used to describe this relationship?
F $c=262-12 p$
G $c=280-12 p$
H $c=262-18 p$
J $c=280-18 p$

Ethan Somes

Numerade Educator

Problem 37

Find the surface area of each sphere. Round to the nearest tenth.
$d=12 \mathrm{ft}$

Ethan Somes

Numerade Educator

Problem 38

Find the surface area of each sphere. Round to the nearest tenth.
$r=41 \mathrm{cm}$

Ethan Somes

Numerade Educator

Problem 39

Find the surface area of each sphere. Round to the nearest tenth.
$r=8.5 \mathrm{in.}$

Ethan Somes

Numerade Educator

Problem 40

Find the surface area of each sphere. Round to the nearest tenth.
$d=18 \mathrm{m}$

Ethan Somes

Numerade Educator

Problem 41

Find the surface area of each cone. Round to the nearest tenth.
slant height $=11 \mathrm{m},$ radius $=6 \mathrm{m}$

Ethan Somes

Numerade Educator

Problem 42

Find the surface area of each cone. Round to the nearest tenth.
diameter $=16 \mathrm{cm},$ slant height $=13.5 \mathrm{cm}$

Ethan Somes

Numerade Educator

Problem 43

Find the surface area of each cone. Round to the nearest tenth.
radius $=5$ in., height $=12$ in.

Ethan Somes

Numerade Educator

Problem 44

Find the surface area of each cone. Round to the nearest tenth.
diameter $=14$ in., height $=24$ in.

Ethan Somes

Numerade Educator

Problem 45

Find $x$ to the nearest tenth. FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 46

Mr. Glover uses a carpenter's square to ind the distance across a stream. The carpenter's find the distance across a stream. The carpenter's square models right angle $N O L .$ He puts the square on top of a pole that is high enough to sight along $\overline{OL}$ to point $P$ across the river. Then he sights along $\overline{O N}$ to point $M .$ If $M K$ is 1.5 feet and $O K=4.5$ feet find the distance $K P$ across the stream.
FIGURE CAN'T COPY.

Ethan Somes

Numerade Educator

Problem 47

Find the area of each polygon with given side length $s$. Round to the nearest hundredth.
Equilateral triangle, $s=7$ in.

Ethan Somes

Numerade Educator

Problem 48

Find the area of each polygon with given side length $s$. Round to the nearest hundredth.
Regular hexagon, $s=12 \mathrm{cm}$

Ethan Somes

Numerade Educator

Problem 49

Find the area of each polygon with given side length $s$. Round to the nearest hundredth.
Regular pentagon, $s=6 \mathrm{m}$

Ethan Somes

Numerade Educator

Problem 50

Find the area of each polygon with given side length $s$. Round to the nearest hundredth.
Regular octagon, $s=50 \mathrm{ft}$

Ethan Somes

Numerade Educator