If two cylinders of equal volumes have their heights in the ratio 2 : 3, then the ratio if their radii is :

Answer: Option D

Let their heights be 2h and 3h and radii be r and R respectively
Then,
$$\begin{array}{rl}& \pi r^2\left(2h\right)=\pi R^2\left(3h\right)\\ & \Rightarrow \frac{r^2}{R^2}=\frac{3}{2}\\ & \Rightarrow \frac{r}{R}=\frac{\sqrt{3}}{\sqrt{2}}i.e.,\sqrt{3}:\sqrt{2}\end{array}$$