Question

Radius of a cylinder is $r$ and height is $h$. Find the change in the volume, if the height remain same and radius is half.

Answer 1

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

$V^{\prime }=\pi {\left(\frac{r}{2}\right)}^{2}h=\frac{{\pi r}^{2}h}{4}$

$\Delta V=V-V^{\prime }={\pi r}^{2}h-\frac{{\pi r}^{2}h}{4}=\frac{3}{4}V$

$\therefore$ Change in volume$=\frac{\Delta V}{V}=\frac{3}{4}$