SOLUTION: The radius of a circle is 1 meter longer than the radius of another circle. If their areas differ by 5 square meters, then what is the radius of each?

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Question 299867: The radius of a circle is 1 meter longer than the radius of another circle. If their areas differ by 5 square meters, then what is the radius of each?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The radius of a circle is 1 meter longer than the radius of another circle.
If their areas differ by 5 square meters, then what is the radius of each?
:
Let r = radius of one circle
then
(r+1) = radius of the other circle
:
Large circle area - small circle area = 5
pi%2A%28r%2B1%29%5E2 - pi%2Ar%5E2 = 5
FOIL
pi%2A%28r%5E2%2B2r%2B1%29 - pi%2Ar%5E2 = 5
divide by pi
r^2 + 2r + 1 - r^2 = 5%2Fpi
r^2 + 2r + 1 - r^2 = 1.59
2r + 1 = 1.59
2r = 1.59 - 1
2r = .59
r = .59%2F2
r = .295 is the radius of the small circle
and 1.295 is the radius of the larger circle
:
:
See if that flies:
pi%2A1.295%5E2 - pi%2A.295%5E2 =
5.27 - .27 = 5