Question

If radius of cone decreases by $50\%$ and its height increases by $20\%$. Then find the percentage change in the volume.

Answer 1

Let initial radius and height of cone be $r$ and $h$ respectively.

Then the final raidus and height will become $r-0.5r$ and $h+0.2h$.

Let the change in volume be $X$

Change in volume$\times$ Volume of Cone without change=Volume of Cone after change

$X\times \frac{1}{3}\times \pi \times r^2\times h$$=\frac{1}{3}\times \pi \times (0.5r{)}^2\times 1.2h$

$X=0.3$

Which means $70$% decrease