A sphere and a cone have the same volume. Each figure has a radius of 3 inches. What is the height of the cone

Question

Kadyn Pearson

Mathematics

27 December, 04:54

A sphere and a cone have the same volume. Each figure has a radius of 3 inches. What is the height of the cone

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Answers (1)

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Mitchell Fuller · Answer 1

Sphere

V = ⁴/₃πr³

V = ⁴/₃ (3.14) (3) ³

V = ⁴/₃ (3.14) (27)

V = ⁴/₃ (84.78)

V = 113.04in³

Cone

V = ¹/₃πr²h

113.04 = ¹/₃ (3.14) (3) ² (h)

113.04 = ¹/₃ (3.14) (9h)

113.04 = ¹/₃ (28.26h)

113.04 = 9.42h

9.42 9.42

12 = h

The height of the cone is 12 inches.