On increasing the diameter of a circle by 40%, its area will be increased by

Question

Philoid · Accepted Answer

Let the radius if circle be r

Area of circle = A = πr²

Radius increases by 40%

So, New Radius r’ = r + 40/100 × r = 1.4r

New Area of circle = A’ = πr’² = π × (1.4r)²

= 1.96πr²

Percentage increase in area =

= = .96 × 100 = 96

∴ Increase in area = 96%