Question

Question 92 (ii)

Radius of a cylinder is r and the height is h. Find the change in the volume if the height is doubled and the radius is halved.

Answer 1

$\because$ Volume of a cylinder $=\pi r^{2}h$
where, h is height and r is radius of base of the cylinder.
If height is doubled and the radius is halved
i.e. h = 2h and $r=\frac{r}{2}$
$\therefore$ Volume $=\pi \times \left(\frac{r}{2}\right)\times \left(\frac{r}{2}\right)\times 2h=\pi \times \frac{r^2}{4}\times 2h=\frac{\pi r^{2}h}{2}$
Hence, volume became half of the original volume.