The ratio of the lengths of the radii of the bases of a right circular cylinder and of a right circular cone is `3:4` and the ratio of their heights is `2:3`, Find the ratio of the volumes of the cylinder and the cone.

Explanation

Let the radii of the bases of the right circular cylinder and the right circular cone are 3r units and 4r units.
Also , let the heights of the cylinder and the cone are 2h units and 3h units.
`therefore` the ratio of the volumes of the right circular cylinder and the right circular cone will be `pi (3r)^2.2h:(1)/(3)pi (4r)^2.3h=pi.9r^2.2h,(1)/(3)pi . 16r^2.3h=(18pir^2h)/(16pir^2h)=18:16=9:8`
Hence the required ratio is `9:8`.