# A right circular cylinder and a right circular cone have the same radius and the same volume

Question:

A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is
(a) 3 : 5
(b) 2 : 5
(c) 3 : 1
(d) 1 : 3

Solution:

(d)  1 : 3
It is given that the right circular cylinder and the right circular cone have the same radius and volume.
Suppose that the radii of their bases are equal to r and the respective heights of the cylinder and the cone are h and H.
As the volumes of the cylinder and the cone are the same, we have:

$\pi r^{2} h=\frac{1}{3} \pi r^{2} H$

$\Rightarrow \frac{h}{H}=\frac{1}{3}$