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

A. $$\sqrt 6 :\sqrt 3 $$

B. $$\sqrt 5 :\sqrt 3 $$

C. $$2 : 3 $$

D. $$\sqrt 3 :\sqrt 2 $$

Answer: Option D

Solution(By Examveda Team)

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