Question

The radius of a solid right circular cylinder increases by $20\%$ and its height decrease by $20\%$. Find the percentage change in its volume.

Answer 1

Let initial radius be r and initial height be h.

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

Final radius $=1.2r$

Final height$=0.8h$

$=\pi (1.2r{)}^{2}h\times 0.8$

$=\pi r^{2}h\times 1.152$

So, its change$=\frac{1.152-1}{1}\times 100$

$=15.2\%$.