Question

If radius of circle is reduced by 10%,then area is diminishd by.

Answer 1

Think of a simple example. Say we have a circle of radius 10cm.

Therefore, area = $\pi r ^{2}$
                          = 100$\pi$.

Now radius decreases by 10%. 10% of 10 is 1. Therefore our new radius is 9cm. 

Therefore, area = $\pi r ^{2}$
                          = 81 $\pi$

Now, let the percentage reduction in area be x%.

Therefore, 100$\pi$ - x$\pi$. = 81 $\pi$

taking $\pi$ common,

             100 - x = 81,
Therefore, x = 19%

Therefore no matter what radius you have(i have solved it for an easier case for better understanding. It works everrywhere), if it is reduced by 10%, the area of the circle reduces by 19%.