On decreasing the radius of a circle by 30%, its area is decreased by

Question

Philoid · Accepted Answer

Let the radius if circle be r

Area of circle = A = πr²

Radius decreases by 30%

So, New Radius r’ = r - 30/100 × r = 0.7r

New Area of circle = A’ = πr’² = π × (0.7r)²

= .49πr²

Percentage decrease in area =

= = .51 × 100 = 51

∴ Decrease in area = 51%