Suppose that a sphere with radius 5a has the same volume as a cone of radius 3a. What is the height of the cone? Give your answer in terms of a. Use the formulas and for the volumes of a sphere and cone respectively.

Question

Davin Sparks

Mathematics

6 September, 02:31

Suppose that a sphere with radius 5a has the same volume as a cone of radius 3a. What is the height of the cone? Give your answer in terms of a. Use the formulas and for the volumes of a sphere and cone respectively.

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Answers (1)

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Howard Reese · Answer 1

Volume of the sphere: [4/3]π (r^3) = [4/3]π (5a) ^3 = [4/3]π*125a^3 =

Volume of the cone: [1/3]π (r^2) H = [1/3]π (3a) ^2 * H = 3πa^2 * H

Volumen of the sphere = Volumen of the cone = >

[4/3]π*125a^3 = 3πa^2 * H = > H = [500/9]a = 55.55 a