Question

A cone and a cylinder are of same height. The radii of their bases are in the ratio $1:2$. Find the ratio their volumes.

Answer 1

It is given that, Height of cone and cylinder are same, let be $h$

Let the radius of cone be $x$

So, radius of cylinder be $2x$

Volume of cone : volume of cylinder

$⟹\frac{1}{3}\pi (x{)}^{2}h:\pi (2x{)}^{2}h$

$⟹\frac{1}{3}\pi (x{)}^{2}h:\pi 4(x{)}^{2}h$

$⟹\frac{1}{3}:4$

$⟹1:12$