Question

The radius of a circle decreases by p%, then by what percentage does the area decrease?

Answer 1

So lets take radius as $r$
So our area is $\pi r^2$
If radius decreases by p%, changed radius is
$\frac{r*(100-p)}{100}$
So area becomes
$\pi (\frac{r*(100-p)}{100})^2 = \pi r^2 ( \frac{100-p}{100} )^2$
$\pi r^2 (1 + \frac{p^2}{10000} - \frac{2*p}{100} )$
$= \pi r^2 ( 1 - ( \frac{2*p- \frac{p^2}{100} }{100} ))$
So decrease in percentage is
$2p - \frac{p^2}{100}$