The heights of two right circular cones are in the ratio 1 : 5 and the perimeter of their bases are in the ratio 5 : 3. Find the ratio of their volumes.

5 : 9

The heights of two right circular cones = 1 : 5

Perimeter of their bases = 5 : 3

We know that the ratio of the perimeter of base is equal to the ratio of the radius of the base of two cones.

So the ratio of the radius = 5 : 3

Now the ratio of their volumes = 5² × 1 : 3² × 5

= 25 : 45 = 5 : 9