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

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 units and the radii of their bases be 3r and r respectively. Then, their volumes are V₁= \(\frac{1}{3}\)π(3r)²×h and V₂= π×r²×3h = \(\frac{V_1}{V_2}\) = \(\frac{3\pi r^2h}{\pi r^2 h}\) = \(\frac{3}{1}\)

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 units and the radii of their bases be 3r and r respectively.

Then,

their volumes are

V₁= \(\frac{1}{3}\)π(3r)²×h and

V₂= π×r²×3h

= \(\frac{V_1}{V_2}\) = \(\frac{3\pi r^2h}{\pi r^2 h}\)

= \(\frac{3}{1}\)