# 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 - Mathematics

MCQ

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

• 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.

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

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 20 Surface Areas and Volume of A Right Circular Cone
Q 10 | Page 25