Page 1 of 4
Volume of Cylinders
BEFORE
Now
WHY?
You found the volume of
rectangular prisms.
You’ll find the volume of
cylinders.
So you can find the volumes of
stacks of coins, as in Ex. 16.
In the Real World
Word Watch
Review Words
cylinder, p. 583
volume, p. 607
Candles You buy two cylindrical candles
with different dimensions. How can you
determine which candle took more wax to
make? In Example 2, you’ll find out by
finding their volumes.
In the previous lesson, you learned that the volume of a rectangular
prism is the product of the area of a base (length width) and the
height. The volume of a cylinder can be found the same way.
The area of the
base is the number
of unit squares that
cover the base.
h
The height is the
number of layers of
unit cubes that fit
in the solid.
Volume of a Cylinder
Words The volume V of a cylinder is the
r
product of the area of a base and the height.
h
Algebra V πr 2h
EXAMPLE
with
Notetaking
You have learned many
properties and formulas
related to solids. Writing
a summary of what you
have learned may help
you prepare for the
chapter test.
1
Finding the Volume of a Cylinder
Find the volume of the cylinder. Use 3.14 for π.
V πr 2h
Write formula for
volume of a cylinder.
2m
3m
≈ (3.14)(2)2(3)
Substitute 3.14 for π, 2 for r,
and 3 for h.
≈ 37.7
Multiply.
ANSWER The volume of the cylinder is about 37.7 cubic meters.
Lesson 12.6
Volume of Cylinders
611
Page 2 of 4
tch Out!
Wa
EXAMPLE
2
Comparing Volumes of Cylinders
4 in.
Make sure to use
the radius, not the diameter,
in the formula for the
volume of a cylinder.
To find which of the candles
from page 611 took more wax
to make, find their volumes.
6 in.
8 in.
5 in.
1 Find the radius of each candle,
which is half of the diameter.
4
2
Tall candle: r 2 in.
6
2
Short candle: r 3 in.
2 Find the volume of each candle. Use 3.14 for π.
Tall candle: V πr 2h
Short candle: V πr 2h
≈ (3.14)(2)2(8)
≈ (3.14)(3)2(5)
≈ 100 in.3
≈ 141 in.3
ANSWER The short candle took more wax to make than the tall candle.
EXAMPLE
3
Finding the Radius of a Cylinder
A cylinder has a height of 9 feet and a volume of 706.5 cubic feet.
Find the radius of the cylinder. Use 3.14 for π.
V πr 2h
with
Review
Need help with solving
equations using square
roots? See p. 533.
Write formula for volume of a cylinder.
706.5 ≈ (3.14)r 2(9)
Substitute 706.5 for V, 3.14 for π, and 9 for h.
706.5 ≈ 28.26r 2
Multiply.
25 ≈ r
2
Divide each side by 28.26.
25
≈r
Take positive square root of each side.
5≈r
Evaluate square root.
ANSWER The radius of the cylinder is about 5 feet.
Your turn now
1.
Find the volume of the cylinder. Use 3.14 for π.
3 cm
2.
5 in.
3.
10 m
2 cm
6 in.
8m
4. Find the radius of a cylinder that has a height of 5 inches and a
volume of 251.2 cubic inches. Use 3.14 for π.
612
Chapter 12
Surface Area and Volume
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 716
Getting Ready to Practice
1. Vocabulary Copy and complete: To find the volume of a cylinder,
multiply the area of a(n) _?_ and the _?_.
Find the volume of the cylinder. Use 3.14 for π.
2.
3.
1 in.
4.
5m
7 mm
4m
11 mm
3 in.
5. Algebra Find the height of a cylinder that has a radius of 3 feet and a
volume of 56.52 cubic feet. Use 3.14 for π.
6. Guided Problem Solving A cheese filled pretzel snack is a cylinder
that has a radius of 1.4 centimeters and a height of 2.2 centimeters.
The cheese center has a radius of 0.6 centimeter and height of
2.2 centimeters. What percent of the snack is cheese?
1 Find the volume of the snack. Use 3.14 for π.
2 Find the volume of the cheese. Use 3.14 for π.
3 What percent of the snack is cheese? Round to the nearest percent.
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
7–9
10–11
12–14
Find the volume of the cylinder. Use 3.14 for π.
7.
8 ft
8.
3 in.
8 ft
9.
8 cm
4 in.
9 cm
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Tell which cylinder has the greater volume.
10. Cylinder A: r 6 m, h 13 m; Cylinder B: r 8 m, h 7.5 m
11. Cylinder C: r 3 yd, h 9 yd; Cylinder D: r 10 ft, h 25 ft
Algebra Find the unknown radius, diameter, or height of the
cylinder. Use 3.14 for π.
12. V 5024 in.3
13. V 25.12 cm3
14. V 5338 ft3
d 16 in.
r _?_
d _?_
h _?_
h 8 cm
h 17 ft
Lesson 12.6
Volume of Cylinders
613
Page 4 of 4
15. Swimming Pools A cylindrical above-ground swimming pool has a
Currency
diameter of 16 feet and a height of 4 feet. A cylindrical kiddie pool has a
diameter of 8 feet and a height of 2 feet. Find the volume of each pool.
Use 3.14 for π. The larger pool can hold 25 tons of water. Write and
solve a proportion to find how much water the smaller pool can hold.
16. Coins The dimensions of different coins are given in the table. To the
nearest hundred cubic millimeters, find the volume of a $1.00 stack of
each coin. Use estimation to check the reasonableness of your answers.
Coin
Penny
Nickel
Dime
Quarter
Diameter (mm)
19.05
21.21
17.91
24.26
Thickness (mm)
1.55
1.95
1.35
1.75
17. Challenge Each tennis ball is a sphere
with a radius of 3.25 centimeters. Find the
volume of the can of tennis balls. Round to
the nearest cubic centimeter.
■
3.25 cm
Coins
The United States Mint
produced 1,296,056,000
golden dollars in 2000. A
golden dollar has a diameter
of 0.0265 m and a thickness
of 0.002 m. What was the
volume of golden dollars
produced that year?
Mixed Review
18. Find the height of a rectangular prism that has a length of 9 inches, a
width of 7 inches, and a volume of 31.5 cubic inches. (Lesson 12.5)
Choose a Strategy Use a strategy from
the list to solve the following exercise.
Explain your choice of strategy.
Problem Solving Strategies
Write an Equation
Guess, Check, and Revise
■ Estimate
■
■
19. What number raised to the fourth
power is equal to 1296?
Basic Skills Find the LCM and the GCF of the numbers.
20. 12, 42
21. 15, 70
22. 96, 120
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
23. Multiple Choice Which of the following are possible dimensions of a
cylinder that has a volume of about 250 cubic units?
A. r 8, h 10 B. r 1, h 4
C. r 2, h 6
D. r 3, h 9
24. Multiple Choice What is the approximate height of a cylinder that has
a diameter of 8 feet and a volume of 502.4 cubic feet?
F. 2.5 ft
614
Chapter 12
Surface Area and Volume
G. 5 ft
H. 10 ft
I. 20 ft