The amount of water in an aquarium is an example of volume. The

of a solid is the number of cubic units contained in its interior. volume

Words Volume 5 (area of base)(height)

Symbols V 5 Bh

VOLUME OF A PRISM

Volume of a Prism The process used in Example 1 can be used to

determine the volume of any prism.

500 Chapter 9 Surface Area and Volume

Goal Find the volumes of prisms

and cylinders.

Key Words• prism p. 483

• cylinder p. 485

• volume

9.49.4 Volume of Prisms and Cylinders

Find the volume of the box by determining

how many unit cubes fit in the box.

Solution

The base is 5 units by 3 units.

So, 3 p 5, or 15 unit cubes are

needed to cover the base layer.

There are 4 layers. Each layer has

15 cubes. So, the total number of

cubes is 4 p 15, or 60.

ANSWER © The volume of the box is 60 cubic units.

EXAMPLE 1 Find the Volume of a Rectangular Prism

5 units

3 units

4 units

unit cube

11

1

h

B

B

h

5 3

Volume of prism 5 area of base 3 height

READING TIP

Volume is measured incubic units, such as ft3,read as “cubic feet.”

Student Help

Page 1 of 8

Find the volume of the prism.

1. 2. 3. 7 in.

10 in.

7 in.5 cm

5 cm5 cm

6 ft

4 ft9 ft

9.4 Volume of Prisms and Cylinders 501

STUDY TIP

Because you aremultiplying three unitsof measure when youfind volume, youranswer will always be in cubic units.

ft 3 ft 3 ft 5 ft3

Student Help

Find Volume of Prisms

Find the volume of the prism.

a. b.

Solution

a. V 5 Bh Write the formula for volume of a prism.

5 (7 p 4) p 5 Area of rectangular base 5 l p w 5 7 p 4.

5 140 Simplify.

ANSWER © The volume is 140 cubic inches.

b. V 5 Bh Write the formula for volume of a prism.

5 1}12

} p 8 p 62 p 3 Area of triangular base 5 }12

} p 8 p 6.

5 72 Simplify.

ANSWER © The volume is 72 cubic feet.

3 ft

6 ft8 ft

5 in.

4 in.7 in.

EXAMPLE 2 Find the Volume of a Prism

Volume of a Cylinder The method for finding the volume of

a cylinder is the same for finding the volume of a prism.

5 3

r

B 5 πr2

h

Volume of cylinder 5 area of base 3 height

Page 2 of 8

502 Chapter 9 Surface Area and Volume

Words Volume 5 (area of base)(height)

Symbols V 5 Bh

5 πr2h

VOLUME OF A CYLINDER

a. How do the radius and height of

the mug compare to the radius

and height of the dog bowl?

b. How many times greater is the

volume of the bowl than the

volume of the mug?

Solution

a. The radius of the mug is 2 inches and the radius of the dog bowl is

6 inches. The radius of the bowl is three times the radius of the mug.

The height of the mug is the same as the height of the bowl.

b. Volume of mug

V 5 πr2h Write the formula for volume.

5 π(22)(4) Substitute for r and for h.

5 16π Simplify.

To compare the volume of the bowl to the volume of the mug, divide

the volume of the bowl by the volume of the mug.

}VV

oo

lluu

mm

ee

oo

ff

bm

ouwgl

}5 }11464π

π} 5 9

ANSWER © The volume of the bowl is nine times the volume of the

mug.

EXAMPLE 3 Compare Volumes of Cylinders

h

Br

Find the volume of the cylinder. Round your answer to the nearest

whole number.

4. 5. 6. 4 m

10 m

1 in.

5 in.3 ft

2 ft

Find Volume of Cylinders

6 in.

4 in.

2 in.

4 in.

Volume of dog bowl

V 5 πr2h

5 π(62)(4)

5 144π

Page 3 of 8

Based upon the units, tell whether the number is a measure of

surface area or volume.

1. 5 ft32. 7 yd2

3. 3 m24. 2 cm3

Candles Find the volume of the candle.

5. 6. 7.

Using Unit Cubes Find the number of unit cubes that will fit in the

box. Explain your reasoning.

8. 9. 10.

Volume of a Prism Find the volume of the prism.

11. 12. 13.

Volume of a Cube In Exercises 14–16, you are given the length

of each side of a cube. Sketch the cube and find its volume.

14. 3 meters 15. 7 feet 16. 10 centimeters

In Exercises 17 and 18, make a sketch of the solid.

Then find its volume.

17. A prism has a square base with 4 meter sides and a height of

7 meters.

18. A prism has a rectangular base that is 3 feet by 6 feet and a height

of 8 feet.

Visualize It!

12 m

9 m

4 m3 cm

6 cm

2 cm

5 in.

4 in.

5 in.

4

23

3

4

4

2

35

Practice and Applications

12 cm

B ≈ 23.4 cm2

6 cm8 cm

10 cm

B ≈ 63.6 cm2

12 cm

Skill Check

Vocabulary Check

Guided Practice

9.4 Volume of Prisms and Cylinders 503

Exercises9.49.4

Example 1: Exs. 8–10Example 2: Exs. 11–18Example 3: Exs. 27–40

Homework Help

Extra Practice

See p. 692.

Page 4 of 8

Finding Volume Find the volume of the combined prisms.

19. 20. 21.

Shopping In Exercises 22–24, use the information about the sizes of

the cereal boxes shown below.

22. Find the volume of each box of cereal.

23. How many small boxes

of cereal do you have to

buy to equal the amount

of cereal in a large box?

24. Which box gives you the

most cereal for your

money? Explain.

Soo Locks In Exercises 25 and 26, use the information below.

Lake Superior is about 22 feet higher than Lake Huron. In order for

ships to safely pass from one lake to the other, they must go through

one of the four Soo Locks.

25. Water is added to the MacArthur Lock until the height is increased by

22 feet. To find the amount of water added to the lock, find the volume

of a rectangular prism with a length of 800 feet, a width of 80 feet, and a

height of 22 feet.

26. How many gallons of water are added to the MacArthur Lock

to raise the ship to the level of Lake Superior? Use the fact that

1 ft3≈ 7.5 gal.

2 m

5 m

7 m

10 m

4 m

2 in.

6 in.

1 in.

1 in.

4 in.

2 in.

2 ft 5 ft

3 ft

2 ft

8 ft

504 Chapter 9 Surface Area and Volume

LakeSuperiorLake

Huron

22 ft800 ft

Not drawn to scale

LakeSuperior

LakeHuron

Top View

Side Viewlower gates upper gates

80 ft

Nutrition

Facts

Serving S

ize 1 bow

l

Serving pe

r contain

er

Amount pe

r servin

g

Calories

45

%Daily Value

Total Fat

0g

Saturated

Fat 0g

Cholester

ol 0mg

Sodium 0m

g

Carbohyd

rate 2g

Dietary F

iber 0g

Sugars 0

g

Protein le

ss than 1

g

Vitamin A

***

Calcium ***

Vitamin C

***

Iron ***

*****

********

********

**

********

********

**

8 in. 2 in.

10 in.

$2.00$2.00Whole

Grain

Cereal

Part of a well balanced breakfast

10 in.

16 in.

4 in.

$6.00$6.00 Nutrit

ion Facts

Serving S

ize 1 bow

l

Serving pe

r containe

r

Amount pe

r servin

g

Calories

45

%Daily Value

Total Fat

0g

Saturated

Fat 0g

Cholester

ol 0mg

Sodium 0m

g

Carbohyd

rate 2g

Dietary Fi

ber 0g

Sugars 0

Protein le

ss than 1

g

Vitamin A

***

Calcium ***

Vitamin C

***

Iron ***

*****

********

********

**

********

********

**

Whole

Grain

Cereal

Part of a well balanced breakfast

HOMEWORK HELP

Extra help with problem

solving in Exs. 19–21 is

at classzone.com

IStudent HelpI C L A S S Z O N E . C O M

SOO LOCKS The first locks

system between Lake Superior

and Lake Huron was built

around 1797. Today, four locks

are available in the Soo Locks

system.

Civil Engineering

Page 5 of 8

Volume of a Cylinder Find the volume of the cylinder. Round your

answer to the nearest whole number.

27. 28. 29.

Swimming Pools In Exercises 30–32, find the volume of the pool.

Round your answer to the nearest whole number. Then compare the

volumes of the pools to answer Exercise 33.

30. 31. 32.

33. Which pool above requires the least amount of water to fill it?

In Exercises 34 and 35, use the information below.

Suppose that a 3-inch by 5-inch index card is rotated around a

horizontal line and a vertical line to produce two different solids.

34. Find the volume of each solid.

35. Which solid has a greater volume? Explain your reasoning.

Aquariums In Exercises 36 and 37, use the information below.

The Giant Ocean Tank at the

New England Aquarium is a

cylinder that is 23 feet deep and

40 feet in diameter as shown.

36. Find the volume of the tank.

37. How many gallons of water

are needed to fill the tank?

(1 ft3≈ 7.5 gal)

38. Personal Aquariums To avoid overcrowding in a personal

aquarium, you should buy one fish for every gallon of

water (231 in.3≈ 1 gal). About how many fish should be in

an aquarium that is a rectangular prism measuring 20 inches

wide, 10 inches long, and is filled with water to a height of

11 inches?

Visualize It!

15 ft

3 ft

24 ft

4 ft4 ft

20 ft

12 m6 m

9 in.

4 in.

9.4 Volume of Prisms and Cylinders 505

5 in.

3 in.

3 in.

5 in.

40 ft

23 ft

AQUARIUM DIVER In

addition to feeding and taking

care of the fish and the plants

in an aquarium, divers make

sure that the tank does not

get too crowded.

Careers

Page 6 of 8

Find the volume of the passenger car of the

Space Spiral at Cedar Point Amusement Park

in Sandusky, Ohio.

Solution

The passenger car is a cylinder with a “hole” in it.

To find the volume, subtract the volume of the hole

from the volume of the larger cylinder.

Volume of larger cylinder 5 πr2h

5 π(102)(14)

≈ 4398

Volume of “hole” 5 πr2h

5 π(42)(14)

≈ 704

ANSWER © The volume of the passenger car is

about 4398 2 704 5 3694 cubic feet.

In Exercises 39 and 40, use the cartons shown.

39. Find the volume of each carton of ice cream.

40. Terry assumes that because the

dimensions doubled, the jumbo

carton contains twice as much ice

cream as the regular carton. Is

Terry right? Explain your reasoning.

You be the Judge

Finding Volume In Exercises 41–43, find the volume of the solid.

41. 42. 43.

Using Algebra Write an expression for the volume of the solid in

terms of x.

44. 45. 46. x

5x

3xx

2x

7

4

x

3

4 m

4 m

4 m

1 m3 ft

8 ft

10 ft8 in.

2 in.

2 in.

6 in.

1 in.

506 Chapter 9 Surface Area and Volume

EXAMPLE Find Volume

10 cm

5 cm

Cool

20 cmJUMBO

10 cm

Cool

HOMEWORK HELP

Extra help with problem

solving in Exs. 41–43 is

at classzone.com

IStudent HelpI C L A S S Z O N E . C O M

14 ft

10 ft 4 ft

Page 7 of 8

9.4 Volume of Prisms and Cylinders 507

Challenge In Exercises 47–49, find the missing dimension(s). If

necessary, round your answer to the nearest whole number.

47. A cylinder has a volume of 100.48 cubic inches and a diameter

of 4 inches. Find the height of the cylinder.

48. A cylinder has a volume of 1538.6 cubic feet and a height of

10 feet. Find the radius of the cylinder.

49. The length of a rectangular prism is twice its width. The height

of the prism equals the width. Find the dimensions of the prism,

given that the volume is 54 cubic inches.

50. Multiple Choice What is the approximate volume of the cylinder

shown at the right?

XA 100 in.3XB 785 in.3

XC 1570 in.3XD 6280 in.3

51. Multiple Choice The volume of the prism shown at the right is

168 cubic feet. What is the height of the prism?

XF 6 feet XG 7 feet

XH 8 feet XJ 9 feet

Using the Pythagorean Theorem Find the unknown side length.

Round your answer to the nearest tenth. (Lesson 4.4)

52. 53. 54.

Surface Area Find the surface area of the solid. If necessary, round

your answer to the nearest whole number. (Lessons 9.2, 9.3)

55. 56. 57.

Solving Equations Solve the equation. (Skills Review, p. 672)

58. x 2 7 5 0 59. m 2 1 5 212 60. 10 1 c 5 23

61. }34

}b 5 24 62. 214d 5 2 63. 6n 5 102

Algebra Skills

5 yd

12 yd8 m

9 m

2 m

7 ft

3 ft

a

18 14b

8

9a

712

Mixed Review

Standardized TestPractice

5 in.

20 in.

x

3 ft7 ft

Page 8 of 8