Question

The base radii of two right circular cones of the same height are in the ratio 3 : 5. Find the ratio of their volumes.

Answer 1

Let $r_1$ and $r_2$ be the radii of two cones and $V_1$ and $V_2$ be their volumes. Let h be the height of the two cones . Then,

$V_1=\frac{1}{3}\pi {r_1}^{2}h$ and $V_2=\frac{1}{3}\pi {r_2}^{2}h$

Therefore,

$\frac{V_1}{V_2}=\frac{{r_1}^2}{{r_2}^2}=\frac{9}{25}$

Hence, the ratio of the volumes of two cones is 9 : 25.