The ratio of the radii of a right circular cylinder cone is 3: 4 and the ratio of their heights is 2:3 Then find the ratio of the volumes of them

Explanation

Let the radii of the cylinder and the cone be 3r unit and 4r unit respectively and their heights be 2h unit and 3h unit respectively .
` :. ` Volume of the cylinder ` = pi xx (3r)^(2) xx 2h` cubic - unit = `18pir^(2)h` cubic - unit
and the volume of the cone ` = 1/3 pi xx (4r)^(2) xx 3h ` cubic - unit = ` 16pir^(2) h ` cubic - unit
Hence the ratio of the volumes of cylinder and the cone is ` 18pir^(2) h : 16pir^(2) h`
` = (18pir^(2)h)/(16pir^(2)h) = 9/8 = 9 :8 `
Hence the required ratio = 9 : 8