Question

If the measure of the radius of the circle is increased by 10% then how many percent is increase in its area

Answer 1

If the measure of the radius of the circle is increased by 10% then the  increase in its area is 21%

Let the initial radius of the circle be 10 cm.

Then its area would be = П(10)² cm² = 100П cm²

Given, radius is increased by 10%.

New radius = (100+10)% of 10 cm

= 110% of 10cm

= [110/100 * 10] cm

= 11 cm

Area of the circle of radius 11cm is П(11)² cm² = 121П cm²

Increase in area = (121П - 100П) cm² = 21П cm²

Percentage increase = [Increase/Initial area) * 100]%  

= [21П/100П) * 100] %

= 21%

This is the required answer.