Two cones have their heights in the ratio 1:3 and the radii of their b

1.	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» 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.

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»

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.