Discussion
The volume of a right circular cylinder and that of a sphere are equal and their radii are also equal. If the height of the cylinder be 'h' and the diameter of the sphere be 'd', which of the following relations is correct?
Answer: D
The correct relation is 3h = 2d.
Set the cylinder's volume equal to the sphere's, with the same radius \(r\):
\[ \begin{aligned} \pi r^{2} h &= \tfrac{4}{3}\pi r^{3} \\ h &= \tfrac{4}{3} r = \tfrac{2}{3} d \end{aligned} \]
since \(d = 2r\). Multiplying by 3 gives \(3h = 2d\). Option C reverses the ratio, and \(h = d\) or \(2h = d\) would make the cylinder too tall or too short to match the sphere's volume.
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