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

let the radii are `r=3x`&`R=x`

and height `h=y`& `H=3y`

so ratio of their volume is `={(1/3)pi(r^2)h}/{(1/3)pi(R^2)H}`

`={(r^2)h}/{(R^2)H}

`={((3x)^2)y}/{(x^2)3y}

`=3/1`

so `3:1`