Question

The radii of the base of a cylinder and a cone are in the ratio 3 : 4. If they have their heights in the ratio 2 : 3, the ratio between their volumes is ______.

Options

• 9 : 8

• 3 : 4

• 8 : 9

• 4 : 3

Answer 1

The radii of the base of a cylinder and a cone are in the ratio 3 : 4. If they have their heights in the ratio 2 : 3, the ratio between their volumes is 9 : 8.

Explanation:

Let the radii of the base of the cylinder and cone be 3r and 4r and their heights be 2h and 3h, respectively.

Then, ratio of their volumes `= (pi(3"r")^2xx(2"h"))/(1/3 pi(4"r")xx(3"h"))`

`=(9"r"^2xx2xx3)/(16"r"^2xx3`

`=9/8`

= 9 : 8