Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:1. Find the ratio of their volumes.

Explanation

Given:
Two cones have their heights in the ratio `1:3` and the radii of their bases in the ratio `3:1`.
Let the heights be `1x` and `3x` respectively and their radii be `3y` and `1y`.
Ratio`=V_1/V_2`
`V_1/V_2=(1/3pi(3y)^2x)/(1/3pi(1y)^2\3x)`
`V_1/V_2=(9y^2timesx)/(y^2xx3x)`
`V_1/V_2=3/1`
Hence, the ratio is `3:1`.