A sphere and a right cylinder have the same radius and volume. The cylinder has a height of 3 inches. Find the radius.

Question

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Answer 1

Volume of sphere = Volume of cylinder

4/3 * PI * R**3 = PI * R**2 * H

substituting 3 for H and dividing both sides of equation by PI:

4/3 * R**3 = 3 * R**2

Multiplying both sides by 3/4:

R**3 = 9/4 * R**2

Dividing both sides by R**2:

R = 9/4 = 2.25

Verification

Volume of sphere = 4/3 * PI * R**3 = 4/3 * 3.14 * 2.25 **3 = 47.7

Volume of cylinder = PI ** R**2 * H = 3.14 * 2.25**2 * 3 = 47.7