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 is the radius of each?

Algebra ->  Polynomials-and-rational-expressions -> 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 is the radius of each?      Log On


   

Question 294843: 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 is the radius of each?
Answer by craigt(10) About Me  (Show Source):
You can put this solution on YOUR website!
a=%28pi%29r%5E2
radius(smaller)=x
radius(Larger)=x+1
a%28smaller%29+=+%28pi%29x%5E2
a%28larger%29+=+%28pi%29%28x%2B1%29%5E2
a%28larger%29+-+a%28smaller%29+=+5%28pi%29m%5E2
Substitute the area equations from above:
%28pi%29%28x%2B1%29%5E2+-+%28pi%29x%5E2+=+5%28pi%29
Divide by pi:
%28x%2B1%29%5E2-x%5E2=5
%28x%5E2%2B2x%2B1%29-x%5E2=5
2x%2B1=5, 2x=4, x=2
Substitute 2 into the two radii equations above:
radius(smaller) = 2, radius(larger)=2+1=3