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 :

A. $$h = d$$

B. $$2h = d$$

C. $$\frac{h}{3} = \frac{d}{2}$$

D. $$\frac{h}{2} = \frac{d}{3}$$

Answer: Option D

Solution(By Examveda Team)

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 $$ = \frac{4}{3}\pi {r^3}$$
$$\eqalign{ & \therefore \pi {r^2}h = \frac{4}{3}\pi {r^3} \cr & \Rightarrow 3h = 4r \cr & \Rightarrow 3h = 2d \cr & \Rightarrow \frac{h}{2} = \frac{d}{3} \cr} $$