The volumes of a sphere and a right circular cylinder having the same radius are equal. The ratio of the diameter of the sphere to the height of the cylinder is?

1 : 2
2 : 1
2 : 3
3 : 2

Correct Answer: 3 : 2

Explanation:

Let r = Radius of cylinder = Radius of sphere, h = Height of the cylinder.
According to the question.
4/3πr³ = πr²h
⇒ h = 4r/3
⇒ 4r = 3h
⇒ 2r = 3/2h
⇒ 2r/h = 3/2
∴ Required ration = 3 : 2

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