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

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Question 148005: The radius of a circle is 1 meter longer than the radius of another circle. If their areas differ by 5 pie square meters, then what us the radius of each?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let r%5B1%5D=radius of first circle and r%5B2%5D=radius of second circle

Since the "radius of a circle is 1 meter longer than the radius of another circle", this means that r%5B1%5D=r%5B2%5D%2B1

So the area of the first circle is
A%5B1%5D=pi%2Ar%5B1%5D%5E2


A%5B1%5D=pi%2A%28r%5B2%5D%2B1%29%5E2 Plug in r%5B1%5D=r%5B2%5D%2B1


A%5B1%5D=pi%2A%28r%5B2%5D%5E2%2B2r%5B2%5D%2B1%29 Foil



The area of the second circle is

A%5B2%5D=pi%2Ar%5B2%5D%5E2


Since "their areas differ by 5 pie square meters", this means that

A%5B1%5D-A%5B2%5D=5pi


pi%2A%28r%5B2%5D%5E2%2B2r%5B2%5D%2B1%29-%28pi%2Ar%5B2%5D%5E2%29=5pi Plug in A%5B1%5D=pi%2A%28r%5B2%5D%5E2%2B2r%5B2%5D%2B1%29 and A%5B2%5D=pi%2Ar%5B2%5D%5E2


pi%28r%5B2%5D%5E2%2B2r%5B2%5D%2B1-r%5B2%5D%5E2%29=5pi Factor out the GCF pi


cross%28pi%29%28r%5B2%5D%5E2%2B2r%5B2%5D%2B1-r%5B2%5D%5E2%29=5cross%28pi%29 Divide both sides by pi


r%5B2%5D%5E2%2B2r%5B2%5D%2B1-r%5B2%5D%5E2=5 Simplify


2r%5B2%5D%2B1=5 Combine like terms.


r%5B2%5D=%284%29%2F%282%29 Divide both sides by 2 to isolate r%5B2%5D.


r%5B2%5D=2 Reduce.


So the radius of the second circle is 2 meters.


r%5B1%5D=r%5B2%5D%2B1 Go back to the first equation


r%5B1%5D=2%2B1 Plug in r%5B2%5D=2


r%5B1%5D=3 Add.



So the radius of the first circle is 3 meters.


note: the two radii can be switched since the problem does not specifically mention the "first" circle or the "second" circle.