Question

A circle's radius is increased by 10%. By what percentage does its area increase

Answer 1

Answer: 21%

Explanation: Let the radius of the circle =R therefore area of the circle = [pi][R * R]
Radius of the circle after 10% increase =R+10% of R=R+R/10=11R/10
Therefore AREA of the circle with radius 11R/10 =[pi][11R/10*11R/10]=[pi][121R*R/100] Hence INCREASE in the AREA of the circle=[pi][121R*R/100]-[pi][R*R] =[pi] [R*R][121/100-1] =[pi][R*R][121-100]/100=[pi][R*R][21]/100 THEREFORE % increase in the area of the circle=[pi][R*R][21/100]/[pi][R*R] whole multiplied by 100=21 HENCE increase in the area of the circle =21% NOTE : pi is a constant whose value=22/7