Question

The base radii of two right circular cones of the same height are in the ratio $2:3$. Find the ratio of their volumes.

• A. $4:1$
• B. $4:9$
• C. $4:7$
• D. $4:11$

Answer 1

The correct option is B $4:9$

Volume of a cone $=\frac{1}{3}\pi r^{2}h$ where $r$ is the radius of the base of the cone and $h$ is the height.
Since height is the same for the two cones, let $r_1$ and h be the radius and height of the first cone and $r_2$ and $h$ be the radius and height of the second cone.
Now, ratio of their volumes is calculated as:
$V_1:V_2$
$=\frac{1}{3}\pi {r_1}^{2}h:\frac{1}{3}\pi {r_2}^{2}h$
$\therefore {r_1}^2:{r_2}^2$ $=2^2:3^2$
$=4:9$

Hence, their volumes are in the ratio $4:9$.