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.
Let the heights of the cones be h and 3h units and the radii of their bases be 3r and r respectively. Then, their volumes are
V1= 
π(3r)2×h and V2= 
π×r2×3h
=
3