Question

The radius and height of a right circular cylinder are each increased by $20\%$. What percentage increase is in the volume?

Answer 1

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

new radius $=r+\frac{20}{100}r$

$=\frac{5}{6}r$

So

$=h+\frac{20}{100}h=\frac{6}{5}h$

Volume $=\pi {\left(\frac{6r}{5}\right)}^2\left(\frac{6}{5}h\right)$

$=\frac{216}{125}\pi r^{2}h$

$\therefore$ Increase in

Volume $=\frac{216}{125}\pi r^{2}h$

$=72.80\%$