Holt CA Course 1

10-2 Volume of Prisms and Cylinders

MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Also covered: MG2.4

California

Standards

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

The volume of a three-dimensional figure is the number of cubes it can hold. Each cube represents a unit of measure called a cubic unit.

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

Height

Triangular prism

Rectangular prism

Cylinder

Base

Height

Base

Height

Base

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

Find the volume of each figure to the nearest tenth.

A.

Additional Example 1: Finding the Volume of Prisms and Cylinders

= 192 ft3

B = 4 • 12 = 48 ft2

V = Bh

= 48 • 4

The base is a rectangle.

Volume of a prism

Substitute for B and h.

Multiply.

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

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

B.

= 192 602.9 in3

B = (42) = 16 in2

V = Bh

= 16 • 12

Additional Example 1: Finding the Volume of Prisms and Cylinders

The base is a circle.

Volume of a cylinder

Substitute for B and h.

Multiply.

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

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

C.

7 ft

V = Bh

= 15 • 7

= 105 ft3

B = • 6 • 5 = 15 ft212

Additional Example 1: Finding the Volume of Prisms and Cylinders

The base is a triangle.

Volume of a prism

Substitute for B and h.

Multiply.

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

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

A.

= 180 in3

B = 6 • 3 = 18 in.2

V = Bh

= 18 • 10

The base is a rectangle.

Volume of prism

Check It Out! Example 1

Substitute for B and h.

Multiply.

10 in.

6 in.3 in.

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

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

B.

8 cm

15 cm

B = (82)

= 64 cm2

= (64)(15) = 960

3,014.4 cm3

Check It Out! Example 1

The base is a circle.

Volume of a cylinderV = Bh

Substitute for B and h.

Multiply.

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

Find the volume of the figure to the nearest tenth.

C.

10 ft

14 ft

12 ft

= 60 ft2

= 60(14)

= 840 ft3

Check It Out! Example 1

The base is a triangle.

Volume of a prism

B = • 12 • 10 12

V = Bh

Substitute for B and h.

Multiply.

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling only 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

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.

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling only 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

By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to 9 times the original volume.

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

A box measures 5 in. by 3 in. by 7 in. Explain whether tripling only the length, width, or height of the box would triple the volume of the box.

Check It Out! Example 2A

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.

Holt CA Course 1

10-2 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

Holt CA Course 1

10-2 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.

Holt CA Course 1

10-2 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 only 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.

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

Check It Out! Example 2B Continued

Tripling the height would triple the volume.

V = 4 • 9 = 36 cm3

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

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

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

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 in3.

Holt CA Course 1

10-2 Volume of Prisms and Cylinders

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

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 in3.

Holt CA Course 1

10-2 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 of the barn is 40,000 ft3.

Additional Example 4: Finding the Volume of Composite Figures

Holt CA Course 1

10-2 Volume of Prisms and CylindersCheck It Out! Example 4

Find the volume of the play house.

3 ft

4 ft

8 ft

5 ft

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

= 96 + 60

V = 156 ft3

Volume of house

Volume of rectangular

prism

Volume of triangular

prism+=

The volume of the play house is 156 ft3.