SOLUTION: A circle and a semicircle have the same area. If the circle has radius 1, what is the radius of the semicircle?

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Question 553370: A circle and a semicircle have the same area. If the circle has radius 1, what is the radius of the semicircle?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Area of a circle: A=+pi%2Ar%5E2

If r=1, then A=pi%2A1%5E2=pi

Area of a semicircle A=%28pi%2Ar%5E2%29%2F2

Since the area of the semicircle is the same as the area of the circle, A=pi.

pi+=+%28pi%2Ar%5E2%29%2F2

Multiply both sides by 2 to clear the fraction:
2pi=+pi%2Ar%5E2

Divide both sides by pi:
2=+r%5E2

r%5E2=2
r=sqrt%282%29 or r=-sqrt%282%29 Reject the negative answer since a radius cannot be negative.

r=sqrt%282%29 Final Answer!!


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