Problema Solution
If the radius of a circle is decreased by 20%, what happens to the area? Be sure to include the percentage of increase/decrease.
Answer provided by our tutors
let
r = the original radius
A = r^2pi is the area
0.80r = the decreased radius by 20% or 80% of the radius
A1 = (0.80)^2 r^2 pi is the area of the decreased circle
A1/A = (0.80)^2 r^2 pi / r^2pi = 0.80^2 = 0.64 or 64%
the area of the new circle is 64% of the area of the original circle or it is decreased by 100 - 64 = 36%.