Question

Choose the correct answer in each of the following :

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

Answer 1

ANSWER:
(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:
$\pi r^{2}h=\frac{1}{3}\pi r^{2}H$
⇒$\frac{h}{H}=\frac{1}{3}$