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Learn to find the volume of pyramids, cones, and

spheres.

If you pour sand from a pyramid-shaped container

into a prism-shaped container with the same

height, base shape, and base size, you will

discover an interesting relationship. The

prism-shaped container appears to hold three

times as much sand as the pyramid-shaped

container.

In fact, the volume of a pyramid is exactly

one-third the volume of a prism that has the same

height, base shape, and base size as the pyramid.

The height of a pyramid is the perpendicular

distance from the pyramids base to its vertex.

Additional Example 1A Finding the Volume of a

Pyramid

Find the volume of the pyramid.

A.

1 3

V

Bh

Use the formula.

3 ft

Find the area of the rectangular base.

B 5 6 30

1 3

6 ft

V

30 3

Substitute for B and h.

5 ft

Multiply.

V 30

The volume is 30 ft3.

Additional Example 1B Finding the Volume of the

Pyramid

Find the volume of the pyramid.

B.

1 3

V

Bh

Use the formula.

Find the area of the triangular base.

1 2

B 2 3 3

1 3

Substitute for B and h.

V

3 5

Multiply.

V 5

The volume is 5 cm3.

Try This Example 1A

Find the volume of the pyramid.

A.

1 3

V

Bh

Use the formula.

4 ft

Find the area of the rectangular base.

B 9 7 63

1 3

V

7 ft

63 4

Substitute for B and h.

9 ft

Multiply.

V 84

The volume is 84 ft3.

Try This Example 1B

Find the volume of the pyramid.

B.

1 3

V

Bh

Use the formula.

h 4 m

Find the area of the triangular base.

1 2

B 3 8 12

1 3

Substitute for B and h.

V

12 4

Multiply.

V 16

3 m

h 8 m

The volume is 16 m3.

The volume of a cone is one-third the volume of a

cylinder with the same height and a congruent

base. The height of a cone is the perpendicular

distance from the cones base to its vertex.

Additional Example 2 Finding the Volume of a Cone

Find the volume of a cone to the nearest tenth.

Use 3.14 for .

1 3

r2h

V

Use the formula.

1 3

3.14 52 6

Substitute.

V

Multiply.

V 157

The volume is about 157.0 yd3.

Try This Example 2

Find the volume of a cone to the nearest tenth.

Use 3.14 for .

1 3

r2h

V

Use the formula.

3 yd

1 3

3.14 22 3

Substitute.

V

Multiply.

V 12.56

2 yd

The volume is about 12.6 yd3.

(No Transcript)

Additional Example 3 Finding the Volume of a

Sphere

Find the volume of the sphere to the nearest

tenth. Use 3.14 for .

4 3

r3

Use the formula.

V

4 3

Substitute.

3.14 73

V

Multiply.

V 1436.026

Round.

V 1436.0

The volume is about 1,436.0 in3.

Try This Example 3

Find the volume of the sphere to the nearest

tenth. Use 3.14 for .

4 3

r3

Use the formula.

V

4 in.

4 3

Substitute.

3.14 43

V

Multiply.

V 267.946

Round.

V 267.9

The volume is about 267.9 in3.

Lesson Quiz

Find the volume of each solid to the nearest

tenth. Use 3.14 for .

301.4 yd3

1. 2.

80 ft3

3. sphere with radius 3 ft 4. 14 ft tall

triangular pyramid whose base triangle has a 12

ft base and a height of 9 ft

113.0 ft3

252 ft3

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