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

A 75%

B 65%

C 35%

D 25%

Correct Answer: Option A

let original radius = r and new radius = (50/100) r = r/2

original area = \(\mathrm{πr}^2\) and new area = \(\mathrm\pi\left(\mathrm r/2\right)^2\)

decrease in area = \(3\mathrm{πr}^2/4\) \(\times\) \(\frac1{\mathrm{πr}^2}\) \(\times\) 100 = 75%