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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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