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The volume V of a cylinder is of the area of the base and the height. Algebra V= πr^2h. Also, this pdf includes Comparing Volumes of Cylinders and Standardized Test Practice.

1.
N

SO

Volume of Cylinders

LES

Goal: Find the volume of cylinders.

Volume of a Cylinder

Words The volume V of a cylinder is the product of r

the area of the base and the height .

h

Algebra V πr 2h

EXAMPLE 1 Standardized Test Practice

What is the volume of the cylinder? Use 3.14 for π.

4m

You

have learned 5m

many properties and

formulas related to

solids. Writing a

summary of what you A 62.8 m3 B 251.2 m3

have learned may help C 314 m3 D 1256 m3

you prepare for the

chapter test. Solution

V πr 2h Write formula for volume of a cylinder.

Substitute 3.14 for π, 4 for r,

3.14 (4)2 5

and 5 for h.

251.2 Multiply.

Answer: The volume of the cylinder is about 251.2 cubic meters .

The correct answer is B . A B C D

274 | Chapter 12 Notetaking Guide

SO

Volume of Cylinders

LES

Goal: Find the volume of cylinders.

Volume of a Cylinder

Words The volume V of a cylinder is the product of r

the area of the base and the height .

h

Algebra V πr 2h

EXAMPLE 1 Standardized Test Practice

What is the volume of the cylinder? Use 3.14 for π.

4m

You

have learned 5m

many properties and

formulas related to

solids. Writing a

summary of what you A 62.8 m3 B 251.2 m3

have learned may help C 314 m3 D 1256 m3

you prepare for the

chapter test. Solution

V πr 2h Write formula for volume of a cylinder.

Substitute 3.14 for π, 4 for r,

3.14 (4)2 5

and 5 for h.

251.2 Multiply.

Answer: The volume of the cylinder is about 251.2 cubic meters .

The correct answer is B . A B C D

274 | Chapter 12 Notetaking Guide

2.
EXAMPLE 2 Comparing Volumes of Cylinders

Tomato Sauce Carlos found two cans of tomato sauce in the pantry. One

can has a diameter of 4 inches and a height of 5 inches. The second one

has a diameter of 3 inches and a height of 6 inches. Which can has the

greater volume?

Solution

WATCH OUT!

1. Find the radius of each can, which is 4 in. 3 in.

Make sure to use the

half of the diameter.

radius, not the diameter,

in the formula for 4

Can 1: r 2 2 in. 5 in.

6 in.

volume of a cylinder.

3

Can 2: r 2 1.5 in.

2. Find the volume of each can. Use 3.14 for π.

Can 1: Can 2:

V πr h 2

V πr 2h

3.14 (2)2 5 3.14 (1.5)2 6

62.8 in.3 42.39 in.3

Answer: Can 1 has the greater volume.

EXAMPLE 3 Finding the Radius of a Cylinder

A cylinder has a height of 12 feet and a volume of 3768 cubic feet. Find

the radius of the cylinder. Use 3.14 for π.

V πr 2h Write formula for volume of a cylinder.

Need

Substitute 3768 for V, 3.14 for π,

help with solving 3768 3.14 r 2 12

equations using and 12 for h.

square roots? See

page 579 of your 3768 37.68r 2 Multiply.

textbook.

100 r 2 Divide each side by 37.68 .

r

100 Take positive square root of each side.

10 r Evaluate square root.

Answer: The radius of the cylinder is about 10 feet .

Lesson 12.6 Volume of Cylinders | 275

Tomato Sauce Carlos found two cans of tomato sauce in the pantry. One

can has a diameter of 4 inches and a height of 5 inches. The second one

has a diameter of 3 inches and a height of 6 inches. Which can has the

greater volume?

Solution

WATCH OUT!

1. Find the radius of each can, which is 4 in. 3 in.

Make sure to use the

half of the diameter.

radius, not the diameter,

in the formula for 4

Can 1: r 2 2 in. 5 in.

6 in.

volume of a cylinder.

3

Can 2: r 2 1.5 in.

2. Find the volume of each can. Use 3.14 for π.

Can 1: Can 2:

V πr h 2

V πr 2h

3.14 (2)2 5 3.14 (1.5)2 6

62.8 in.3 42.39 in.3

Answer: Can 1 has the greater volume.

EXAMPLE 3 Finding the Radius of a Cylinder

A cylinder has a height of 12 feet and a volume of 3768 cubic feet. Find

the radius of the cylinder. Use 3.14 for π.

V πr 2h Write formula for volume of a cylinder.

Need

Substitute 3768 for V, 3.14 for π,

help with solving 3768 3.14 r 2 12

equations using and 12 for h.

square roots? See

page 579 of your 3768 37.68r 2 Multiply.

textbook.

100 r 2 Divide each side by 37.68 .

r

100 Take positive square root of each side.

10 r Evaluate square root.

Answer: The radius of the cylinder is about 10 feet .

Lesson 12.6 Volume of Cylinders | 275

3.
Guided Practice Find the volume of the cylinder. Use 3.14 for π.

1. 2. 6 in.

3. 8m

2 cm

1 cm

9 in. 6m

12.56 cm3 1017.36 in.3 301.44 m3

4. Find the radius of a cylinder that has a height of 7 inches and a volume

of 351.68 cubic inches. Use 3.14 of π.

4 in.

276 | Chapter 12 Notetaking Guide

1. 2. 6 in.

3. 8m

2 cm

1 cm

9 in. 6m

12.56 cm3 1017.36 in.3 301.44 m3

4. Find the radius of a cylinder that has a height of 7 inches and a volume

of 351.68 cubic inches. Use 3.14 of π.

4 in.

276 | Chapter 12 Notetaking Guide