Question

The radius of the base of a right circular cylinder is halved and the height is doubled . What is the ratio of the volume of the new cylinder to that of the original cylinder ?

Answer 1

Let,

Height of the right circular cylinder $=H$

Radius of the base of the cylinder $=R$

Therefore,

Volume of the cylinder, $V=\pi R^{2}H$

Now,

New height of the right circular cylinder $H^{\prime }=2H$

New radius of the base of the cylinder $R^{\prime }=\frac{R}{2}$

Therefore,

New volume of the cylinder, $V^{\prime }=\pi R^{\prime 2}{H}^{\prime }$

$=\pi \frac{R^2}{4}2H$

Therefore,

Required ratio $=\frac{V^{\prime }}{V}$

$=\frac{\pi \frac{R^2}{4}2H}{\pi R^{2}H}$

$=\frac{1}{2}$

$=1:2$

Therefore, the ratio of the volume of the new cylinder to that of the origional cylinder is $2:1$.