Question

Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3:1.Show that their volumes are in the ratio 3 : 1.

Answer 1

Let the heights be 1x and 3x respectively
and their radii be 3y and 1y .
$ratio=\frac{\text{volume of cone1}}{\text{volume of cone 2}}=\frac{\frac{1}{3}\pi (3y{)}^{2}x}{\frac{1}{3}\pi (1y{)}^{2}3x}=\frac{9y^2\times x}{y^2\times 3x}=\frac{3}{1}$