Question

Two cones have the same volume and their base radii are in the ratio $3:4$. What is the ratio of their heights?

• A. $9:25$
• B. $16:25$
• C. $25:16$
• D. $16:9$

Answer 1

The correct option is D

$16:9$

Let the radii of the first and the second cone be $3r$ and $4r$ respectively. Also, let the heights of the first and the second cone be $h_1$ and $h_2$ be respectively.
Since the volumes are equal, we have

$\frac{1}{3}\pi (3r{)}^2\times h_1=\frac{1}{3}\pi (4r{)}^2\times h_2$
Thus, $\frac{h_1}{h_2}=\frac{16}{9}$.
Therefore, the required ratio is $16:9$.