Question

A right cylinder and a right circular cone have the equal radii and equal volumes. Then, 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 the cylinder and the cone of equal volumes, and $h_{1}and{h}_2$ be their heights respectively.

$Volumeofcylinder=\pi r^2{h}_1$
$Volumeofcone=\frac{1}{3}\pi r^2{h}_2$

As per the data,
$\pi r^2{h}_1=\frac{1}{3}\pi r^2{h}_2\Rightarrow h_1=\frac{1}{3}{h}_2\Rightarrow \frac{h_1}{h_2}=\frac{1}{3}\therefore h_1:h_2=1:3$