The curved surface area of a cylinder is 264 $m^2$ and its volume is 924 $m^3$. Find the ratio of its height to its diameter.

The correct option is C. $\frac{3}{7}$

Curved surface area of cylinder = $2\pi rh$

Volume of a cylinder = $\pi r^{2}h$

$\Rightarrow \frac{\pi r^{2}h}{2\pi rh}=\frac{924}{264}\Rightarrow \frac{r}{2}=\frac{7}{2}$

$\therefore r=7$ m

Curved surface area of cylinder = $2\pi rh$

$\Rightarrow 2\times \frac{22}{7}\times 7\times h=264$

$\Rightarrow h=\frac{264}{44}$

$\therefore h=6$ m

So,$\frac{h}{2r}=\frac{6}{14}=\frac{3}{7}$