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

#### Options

3 : 5

2 : 5

3 : 1

1 : 3

#### Solution

It is given that the volumes of both the cylinder and the cone are the same.

So, let Volume of the cylinder = Volume of the cone = *V*

It is also given that their base radii are the same.

So, let Radius of the cylinder = Radius of the cone

= *r*

Let the height of the cylinder and the cone be `h_"cylinder"` and `h_"cone "` respectively.

The formula of the volume of a cone with base radius ‘*r*’ and vertical height ‘*h*’ is given as

Volume of cone = `1/3 pi r^2h`

The formula of the volume of a cylinder with base radius ‘*r*’ and vertical height ‘*h*’ is given as

Volume of cylinder = `pi r^2h`

So we have `(h_"cylinder")/(h_"cone")=(Vpir^2)/(3V pi r^2)`

`(h_"cylinder")/(h_"cone")=1/3`