8-5 Volume of Prisms and Cylinders

Course 3

Warm Up

Problem of the Day

Lesson Presentation

Warm Up

Find the area of each figure described. Use 3.14 for .

1. a triangle with a base of 6 feet and a height of 3 feet

2. a circle with radius 5 in.

Course 3

8-5 Volume of Prisms and Cylinders

9 ft2

78.5 ft2

Problem of the Day

You are painting identical wooden cubes red and blue. Each cube must have 3 red faces and 3 blue faces. How many cubes can you paint that can be distinguished from one another?only 2

Course 3

8-5 Volume of Prisms and Cylinders

Learn to find the volume of prisms and cylinders.

Course 3

8-5 Volume of Prisms and Cylinders

Vocabulary

cylinder

prism

Insert Lesson Title Here

Course 3

8-5 Volume of Prisms and Cylinders

Course 3

8-5 Volume of Prisms and Cylinders

A cylinder is a three-dimensional figure that has two congruent circular bases. 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.

Course 3

8-5 Volume of Prisms and Cylinders

Height

Triangular prism

Rectangular prism

Cylinder

Base

Height

Base

Height

Base

Course 3

8-5 Volume of Prisms and Cylinders

VOLUME OF PRISMS AND CYLINDERSWords Numbers Formula

Prism: The volume V of a prism is the area of the base B times the height h.

Cylinder: The volume of a cylinder is the area of the base B times the height h.

B = 2(5)= 10 units2

V = 10(3)

= 30 units3

B = (22)= 4 units2

V = (4)(6) = 24 75.4 units3

V = Bh

V = Bh

= (r2)h

Course 3

8-5 Volume of Prisms and Cylinders

Area is measured in square units. Volume is measured in cubic units.

Remember!

Find the volume of each figure to the nearest tenth. Use 3.14 for .

Additional Example 1A: Finding the Volume of Prisms and Cylinders

Course 3

8-5 Volume of Prisms and Cylinders

a rectangular prism with base 2 cm by 5 cm and height 3 cm

= 30 cm3

B = 2 • 5 = 10 cm2

V = Bh

= 10 • 3

Area of base

Volume of a prism

Find the volume of the figure to the nearest tenth. Use 3.14 for .

Course 3

8-5 Volume of Prisms and Cylinders

4 in.

12 in.

= 192 602.9 in3

B = (42) = 16 in2

V = Bh

= 16 • 12

Additional Example 1B: Finding the Volume of Prisms and Cylinders

Area of base

Volume of a cylinder

Find the volume of the figure to the nearest tenth. Use 3.14 for .

Course 3

8-5 Volume of Prisms and Cylinders

5 ft

7 ft

6 ft

V = Bh

= 15 • 7

= 105 ft3

B = • 6 • 5 = 15 ft212

Additional Example 1C: Finding the Volume of Prisms and Cylinders

Area of base

Volume of a prism

Find the volume of the figure to the nearest tenth. Use 3.14 for .

Course 3

8-5 Volume of Prisms and Cylinders

A rectangular prism with base 5 mm by 9 mm and height 6 mm.

= 270 mm3

B = 5 • 9 = 45 mm2

V = Bh

= 45 • 6

Area of base

Volume of prism

Check It Out: Example 1A

Find the volume of the figure to the nearest tenth. Use 3.14 for .

Course 3

8-5 Volume of Prisms and Cylinders

8 cm

15 cm

B = (82)

= 64 cm2

= (64)(15) = 960

3,014.4 cm3

Check It Out: Example 1B

Area of base

Volume of a cylinderV = Bh

Find the volume of the figure to the nearest tenth. Use 3.14 for .

Course 3

8-5 Volume of Prisms and Cylinders

10 ft

14 ft

12 ft

= 60 ft2

= 60(14)

= 840 ft3

Check It Out: Example 1C

Area of base

Volume of a prism

B = • 12 • 10 12

V = Bh

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.

Additional Example 2A: Exploring the Effects of Changing Dimensions

Course 3

8-5 Volume of Prisms and Cylinders

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.

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.

Additional Example 2B: Exploring the Effects of Changing Dimensions

Course 3

8-5 Volume of Prisms and Cylinders

By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.

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.

Check It Out: Example 2A

Course 3

8-5 Volume of Prisms and Cylinders

Tripling the length would triple the volume.

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

The original box has a volume of (5)(3)(7) = 105 cm3.

Course 3

8-5 Volume of Prisms and Cylinders

Check It Out: Example 2A Continued

The original box has a volume of (5)(3)(7) = 105 cm3.

Tripling the height would triple the volume.

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

Course 3

8-5 Volume of Prisms and Cylinders

Check It Out: Example 2A Continued

Tripling the width would triple the volume.

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

The original box has a volume of (5)(3)(7) = 105 cm3.

Course 3

8-5 Volume of Prisms and Cylinders

By tripling the radius, you would increase the volume nine times.

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.

Check It Out: Example 2B

V = 36 • 3 = 108 cm3

The original cylinder has a volume of 4 • 3 = 12 cm3.

Check It Out: Example 2B Continued

Course 3

8-5 Volume of Prisms and Cylinders

Tripling the height would triple the volume.

V = 4 • 9 = 36 cm3

The original cylinder has a volume of 4 • 3 = 12 cm3.

A drum company advertises a snare drum that is 4 inches high and 12 inches in diameter. Estimate the volume of the drum.

Additional Example 3: Music Application

Course 3

8-5 Volume of Prisms and Cylinders

d = 12, h = 4

r = = = 6

Volume of a cylinder.

d 2V = (r2)h

12 2

= (3.14)(6)2 • 4

= (3.14)(36)(4)

= 452.16 ≈ 452

Use 3.14 for .

The volume of the drum is approximately 452 in.2

A drum company advertises a bass drum that is 12 inches high and 28 inches in diameter. Estimate the volume of the drum.

Check It Out: Example 3

Course 3

8-5 Volume of Prisms and Cylinders

d = 28, h = 12

r = = = 14

Volume of a cylinder.

d 2V = (r2)h

28 2

= (3.14)(14)2 • 12

= (3.14)(196)(12)

= 7385.28 ≈ 7,385

Use 3.14 for .

The volume of the drum is approximately 7,385 in.2

Course 3

8-5 Volume of Prisms and Cylinders

Find the volume of the the barn.

Volume of barn

Volume of rectangular

prism

Volume of triangular

prism+=

= 30,000 + 10,000

V = (40)(50)(15) + (40)(10)(50)12

= 40,000 ft3

The volume is 40,000 ft3.

Additional Example 4: Finding the Volume of Composite Figures

Check It Out: Example 4

Course 3

8-5 Volume of Prisms and Cylinders

Find the volume of the house.

3 ft

4 ft

8 ft

5 ft

= (8)(3)(4) + (5)(8)(3)12

= 96 + 60

V = 156 ft3

Volume of house

Volume of rectangular

prism

Volume of triangular

prism+=

Lesson QuizFind the volume of each figure to the nearest tenth. Use 3.14 for .

306 in3942 in3

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160.5 in3

No; the volume would be quadrupled because you have to use the square of the radius to find the volume.

Course 3

8-5 Volume of Prisms and Cylinders

10 in.

8.5 in.3 in.

12 in.12 in.

2 in.

15 in.10.7 in.

1. 3.2.

4. Explain whether doubling the radius of the cylinder above will double the volume.