SOLUTION: The number of centimeters in the perimeter of a semicircle is numerically the same as the number of square centimeters in its area. What is the number of centimeters in the radiu

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Question 332758: The number of centimeters in the perimeter of a semicircle is numerically the
same as the number of square centimeters in its area. What is the number of
centimeters in the radius of the semicircle?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The number of centimeters in the perimeter of a semicircle is numerically the
same as the number of square centimeters in its area.
What is the number of centimeters in the radius of the semicircle?
:
Let r = the radius
Half the circumference = pi%2Ar
:
Circumference of a semi-circle = area of the semicircle
%28pi%2Ar%29%2B+2r = .5%2Api%2Ar%5E2
factor out r
r%28pi%2B2%29 = .5%2Api%2Ar%5E2
Divide both sides by r
pi%2B2 = .5%2Api%2Ar
Use 3.1416 for pi
3.1416 + 2 = .5*3.1416*r
5.1416 = 1.5708r
r = 5.1416%2F1.5708
r = 3.273 cm is the radius
:
:
Check this:
find the area of the semi circle
A = .5%2Api%2A3.273%5E2
A = 16.827
:
Find the circum of the semi circle
C = %28pi%2A3.273%29%2B2%282.373%29
C = 16.828, close enough