A right circular cylinder and a sphere are of equal volumes and their radii are also equal. If h is the height of the cylinder and d is the diameter of the sphere then

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\frac{h}{3} = \frac{d}{2}

\frac{h}{2} = \frac{d}{3}

2 h = d

h = d

answer is B.

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Detailed Solution

Given a right circular cylinder and a sphere are of equal volumes and their radii are also equal.
We know that,
Volume of a sphere

= 43 π R 3

, where R is the radius. Volume of a cylinder

π r 2 h

, where r is the radius and h is its height.
According to given condition,
Volume of cylinder = Volume of sphere
Radius of cylinder = radius of sphere
Let d be the diameter of sphere.
Therefore,

R = r = d 2

So,

\Rightarrow π {(\frac{d}{2})}^{2} h = \frac{4}{3} π {(\frac{d}{2})}^{3}

\Rightarrow h = \frac{2}{3} d

\Rightarrow \frac{h}{2} = \frac{d}{3}

Therefore,

h 2 = d 3 .

Hence option (2) is correct.

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