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 :
Options:
A . $$h = d$$
B . $$2h = d$$
C . $$\frac{h}{3} = \frac{d}{2}$$
D . $$\frac{h}{2} = \frac{d}{3}$$
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 $$ = \frac{4}{3}\pi {r^3}$$ $$\eqalign{ & \therefore \pi {r^2}h = \frac{4}{3}\pi {r^3} \cr & \Rightarrow 3h = 4r \cr & \Rightarrow 3h = 2d \cr & \Rightarrow \frac{h}{2} = \frac{d}{3} \cr} $$
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