SOLUTION: If the radius of a circular region were decreased by 20 percent, the area of the circular region would decrease by what percent? A 16% b 20% c 36% d 44%

Algebra ->  Circles -> SOLUTION: If the radius of a circular region were decreased by 20 percent, the area of the circular region would decrease by what percent? A 16% b 20% c 36% d 44%       Log On


   

Question 274809: If the radius of a circular region were decreased by 20 percent, the area of the circular region would decrease by what percent?
A 16% b 20% c 36% d 44%
Answer by dabanfield(803) About Me  (Show Source):
You can put this solution on YOUR website!
If the radius of a circular region were decreased by 20 percent, the area of the circular region would decrease by what percent?
If R is the original radius then the area of the circle is pi*R^2
If we decrease the radius by 20% the new radius is .8*R so the new area is:
pi*(.8*R)^2 = pi*(.64*R^2).
Compute the percent of the new to the old:

(pi*.64R^2)/(pi*R^2) = .64
The decrease then is 100 - 64 = 36%