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, the diameter of the sphere, then :

Answer: Option D

Let the radius of the sphere and that of the right circular cylinder be r
Then,
Volume of the cylinder $$=\pi r^{2}h$$
Volume of the sphere $$=\frac{4}{3}\pi r^3$$
$$\begin{array}{rl}& \therefore \pi r^{2}h=\frac{4}{3}\pi r^3\\ & \Rightarrow 3h=4r\\ & \Rightarrow 3h=2d\\ & \Rightarrow \frac{h}{2}=\frac{d}{3}\end{array}$$