Question

The radius of a circle is increased by 50. By what % will its area be increased ?

Answer 1

Let initial radius was 100
Area = pi * R * R = 3.14 * 100 * 100 = 21400 sq.unit.
New radius = 100 + 50% of 100 = 150
New area = pi * R * R = 3.14 * 150 * 150 = 70650
Increased Area = 70650 - 31400 = 39250
% Increased Area = (39250 * 100)/31400 = 125%
Short Cut:
Let initial area = 100
100===50% (first radius increase)==150===50% (second radius increase)===>225
So, Increase Area = 125%