The area of a circle was reduced by 10%.find the corresponding percentage decrease in the radius
The area of two circles is proportional to the square of the radii.
.9area/1area = r1^2 / r2^2
(r1/r2)^2 = .9
r1/r2 = √.9 = appr .949
so it is reduced by 5.1%
another way:
take a specific case
suppose the radius is 12 cm
then the area is 144π cm^2
If we reduce that area by 10% we are left with 129.6π cm^2
πr^2 = 129.6π
r^2 = 129.6
r = 11.3842
and 11.3842/12 = .94868
which shows a decrease of 1 - .94868 or appr .051
which would be 5.1%