Question

The radius and height of a cylinder are increased by $10\%$, then what will be the percentage increase in volume?

Answer 1

Let the original radius be $‘r^{\prime }$

Now, increased radius $=r+10\%\times r=1+0.1r=1.1r$

Let the original height be $h$

Now, increased height $=h+10\%\times h=1+0.1h=1.1h$

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

New Volume $=\pi \left(1.1r{)}^2\right(1.1h{)}^2=1.331\pi r^{2}h$

Percentage increase in volume $=\frac{1.331\pi r^{2}h-\pi r^{2}h}{\pi r^{2}h}\times 100\%$

$=\frac{0.331\pi r^{2}h}{\pi r^{2}h}\times 100\%$

$=33.1\%$