Question

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.

Answer 1

Let the heights of the cones be h and 3h and radii of their bases be 3r and r respectively. Then, their volumes are 

Volume of first cone (V₁) = \(\frac{1}{3}\)π(3r)²h 

Volume of second cone (V₂) = \(\frac{1}{3}\)πr²(3h) 

Now, V₁/V₂ = \(\frac{3}{1}\) 

Ratio of two volumes is 3:1.