Question

If the radius of a circle is decreased by 50% then percentage decrease in area.

Answer 1

Let original radius $=R$

new radius $=\frac{50}{100}R=\frac{R}{2}$

Original area $={\pi R}^2$

New area $=\left\{\pi {\left(\frac{R}{2}\right)}^2\right\}=\frac{\pi R^2}{4}$

Decrease in area $=(\frac{3\pi R^2}{4}\times \frac{1}{\pi R^2}\times 100)$% $=75$%