Question

If the radius of a cylinder is doubled and height is halved find the change in the volume.

Answer 1

Let the radius of the cylinder be $r$ and height be $h$.

Then, volume of the cylinder,
$V_1=\pi r^{2}h$

New radius, $R=2r$

New height of the cylinder, $H=\frac{h}{2}$

$\therefore$ Volume of a cylinder,
$V_2=\pi R^{2}H=\pi (2r{)}^2\frac{h}{2}$

$=\pi \times 4r^2\times \frac{h}{2}$

$=2\pi r^{2}h$

$=2V_1$

Hence, if the radius of a cylinder is doubled and height of a cylinder is halved, the volume of the cylinder is doubled.