Question

A right cylinder and a right circular cone have the same radius and same volumes.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

The correct option is D

1:3

Let r be the radius of cylinder and cone of equal volumes and $h_{1}and{h}_2$ be their heights.

$\therefore Volumeofcylinder=\pi r^2{h}_1$

and volume of cone=$\frac{1}{3}\pi r^2{h}_2\Rightarrow \pi r^2{h}_1=\frac{1}{3}\pi r^2{h}_2\Rightarrow h_1=\frac{1}{3}{h}_2\Rightarrow \frac{h_1}{h_2}=\frac{1}{3}\therefore h_1:h_2=1:3$