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6-6

Volume of Prisms and Cylinders

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra

Warm Up Make a sketch of a closed book using

two-point perspective.

Warm Up Make a sketch of a closed book using

two-point perspective.

Possible answer

Math

Learn to find the volume of prisms and cylinders.

Vocabulary

prism cylinder

A prism is a three-dimensional figure named for

the shape of its bases. The two bases are

congruent polygons. All of the other faces are

parallelograms. A cylinder has two circular

bases.

Rectangular prism

Cylinder

Triangular prism

Height

Height

Height

Base

Base

Base

VOLUME OF PRISMS AND CYLINDERS

B 2(5)

10 units2

V Bh

V 10(3)

30 units3

B p(22)

V Bh

4p units2

(pr2)h

V (4p)(6) 24p

? 75.4 units3

(No Transcript)

Additional Example 1A Finding the Volume of

Prisms and Cylinders

Find the volume of each figure to the nearest

tenth.

A. A rectangular prism with base 2 cm by 5 cm and

height 3 cm.

B 2 5 10 cm2

Area of base

Volume of a prism

V Bh

10 3

30 cm3

Additional Example 1B Finding the Volume of

Prisms and Cylinders

Find the volume of the figure to the nearest

tenth.

B.

B p(42) 16p in2

Area of base

4 in.

Volume of a cylinder

V Bh

12 in.

16p 12

192p ? 602.9 in3

Additional Example 1C Finding the Volume of

Prisms and Cylinders

Find the volume of the figure to the nearest

tenth.

C.

Area of base

5 ft

V Bh

Volume of a prism

15 7

105 ft3

7 ft

6 ft

Try This Example 1A

Find the volume of the figure to the nearest

tenth.

A. A rectangular prism with base 5 mm by 9 mm and

height 6 mm.

B 5 9 45 mm2

Area of base

Volume of prism

V Bh

45 6

270 mm3

Try This Example 1B

Find the volume of the figure to the nearest

tenth.

B p(82)

Area of base

B.

8 cm

64p cm2

Volume of a cylinder

V Bh

15 cm

(64p)(15) 960p

? 3,014.4 cm3

Try This Example 1C

Find the volume of the figure to the nearest

tenth.

C.

Area of base

10 ft

60 ft2

Volume of a prism

V Bh

60(14)

14 ft

840 ft3

12 ft

Additional Example 2A Exploring the Effects of

Changing Dimensions

A juice box measures 3 in. by 2 in. by 4 in.

Explain whether tripling the length, width, or

height of the box would triple the amount of

juice the box holds.

The original box has a volume of 24 in3. You

could triple the volume to 72 in3 by tripling any

one of the dimensions. So tripling the length,

width, or height would triple the amount of juice

the box holds.

Additional Example 2B Exploring the Effects of

Changing Dimensions

A juice can has a radius of 2 in. and a height of

5 in. Explain whether tripling the height of the

can would have the same effect on the volume as

tripling the radius.

By tripling the height, you would triple the

volume. By tripling the radius, you would

increase the volume to nine times the original.

Try This Example 2A

A box measures 5 in. by 3 in. by 7 in. Explain

whether tripling the length, width, or height of

the box would triple the volume of the box.

The original box has a volume of (5)(3)(7) 105

cm3.

V (15)(3)(7) 315 cm3

Tripling the length would triple the volume.

Try This Example 2A

A box measures 5 in. by 3 in. by 7 in. Explain

whether tripling the length, width, or height of

the box would triple the volume of the box.

The original box has a volume of (5)(3)(7) 105

cm3.

V (5)(3)(21) 315 cm3

Tripling the height would triple the volume.

Try This Example 2A

A box measures 5 in. by 3 in. by 7 in. Explain

whether tripling the length, width, or height of

the box would triple the volume of the box.

The original box has a volume of (5)(3)(7) 105

cm3.

V (5)(9)(7) 315 cm3

Tripling the width would triple the volume.

Try This Example 2B

A cylinder measures 3 cm tall with a radius of 2

cm. Explain whether tripling the radius or height

of the cylinder would triple the amount of volume.

The original cylinder has a volume of 4? 3

12? cm3.

V 36? 3 108? cm3

By tripling the radius, you would increase the

volume nine times.

Try This Example 2B

A cylinder measures 3 cm tall with a radius of 2

cm. Explain whether tripling the radius or height

of the cylinder would triple the amount of volume.

The original cylinder has a volume of 4? 3

12? cm3.

V 4? 9 36? cm3

Tripling the height would triple the volume.

Additional Example 3 Construction Application

A section of an airport runway is a rectangular

prism measuring 2 feet thick, 100 feet wide, and

1.5 miles long. What is the volume of material

that was needed to build the runway?

length 1.5 mi 1.5(5280) ft

7920 ft

The volume of material needed to build the runway

was 1,584,000 ft3.

width 100 ft

height 2 ft

V 7920 100 2 ft3

1,584,000 ft3

Try This Example 3

A cement truck has a capacity of 9 yards3 of

concrete mix. How many truck loads of concrete to

the nearest tenth would it take to pour a

concrete slab 1 ft thick by 200 ft long by 100 ft

wide?

B 200(100)

20,000 ft2

V 20,000(1)

20,000 ft3

27 ft3 1 yd3

Additional Example 4 Finding the Volume of

Composite Figures

Find the volume of the the barn.

30,000 10,000

40,000 ft3

The volume is 40,000 ft3.

Try This Example 4

Find the volume of the figure.

5 ft

96 60

4 ft

V 156 ft3

8 ft

3 ft

Lesson Quiz

Find the volume of each figure to the nearest

tenth. Use 3.14 for p.

10 in.

2 in.

1.

3.

2.

12 in.

12 in.

10.7 in.

15 in.

3 in.

8.5 in.

942 in3

306 in3

160.5 in3

4. Explain whether doubling the radius of the

cylinder above will double the volume.

No the volume would be quadrupled because you

have to use the square of the radius to find the

volume.

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