The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³. Find the ratio of its diameter to its height.

A. 3 : 7

B. 7 : 3

C. 6 : 7

D. 7 : 6

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & \frac{{\pi {r^2}h}}{{2\pi rh}} = \frac{{924}}{{264}} \cr & \Rightarrow r = \left( {\frac{{924}}{{264}} \times 2} \right) \cr & \Rightarrow r = 7\,m \cr} $$
And,
$$\eqalign{ & \therefore 2\pi rh = 264 \cr & \Rightarrow h = \left( {264 \times \frac{7}{{22}} \times \frac{1}{2} \times \frac{1}{7}} \right) \cr & \Rightarrow h = 6\,m \cr} $$
∴ Required ratio :
$$ = \frac{{2r}}{h} = \frac{{14}}{6} = 7:3$$