Page 45 - Math Course 3 (Book 2)

Volume of Pyramids, Cones, and Spheres

Volume of a Sphere

Example

12 in. Find the volume of the sphere. Round to the
nearest tenth.

15 in.

15 in.

1 Formula for volume of a 5 ft
V = Bh
3 pyramid

1
V = (15 • 15)h The base is a square, so 4
3 B = 15 • 15. V = π³ Formula for volume of a sphere
3
1 The height of the pyramid is
V = (15 • 15)12 4
3 12 inches. V = • π • 5³ Replace r with 5
3
V = 900 Simplify.
≈ 523.6 ft³ Simplify.

The volume is 900 cubic The volume of the sphere is
Answer Answer
inches. about 523.6 cubic feet.

Volume of a Cone Real World Example

Example LANDSCAPING
When mulch was dumped from a truck, it formed
a cone-shaped mound with a diameter of 15 feet
and a height of 8 feet. What is the volume of the
Find the volume of the cone. Round to the nearest mulch?
tenth.

8 m

5.5 m

1
V = π²h Formula for volume of a cone
3 1
Estimate • 3 • 8² • 8 = 512
3
1
V = • (5 • 5)² • 8 Replace r with 5.5 and h with 1 Formula for the volume of a
3 8. V = πr²h cone
3
1 Since d = 15, replace r with
V ≈ 253.4 Simplify. V = • π • (7.5)² • 8 7.5. Replace h with 8.
3
V ≈ 471 Simplify.

The volume is about 253.4 The volume of the mulch is
Answer Answer
cubic meters. about 471 cubic feet.

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