SOLUTION: 94. Areas of two circles. 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?

Algebra ->  Circles -> SOLUTION: 94. Areas of two circles. 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?      Log On


   

Question 363723: 94. Areas of two circles. 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?
Found 2 solutions by robertb, ankor@dixie-net.com:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
I will assume the following problem: Areas of two circles. The radius of a circle is 1 meter
longer than the radius of another circle. If their areas differ
by 5pisquare meters, then what is the radius of each?
Then the answer is as follows:
pi%28r%2B1%29%5E2+-+pi%2Ar%5E2+=+5pi. Clearing the equation of pi and simplifying, r%5E2%2B2r+%2B+1+-+r%5E2+=+5,
2r+%2B+1+=+5,
or r = 2 meters, the radius of the smaller circle, and r +1 = 3 meters, the radius of the bigger circle.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Areas of two circles. 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?
:
Two radii, r, (r+1)
pi%2A%28r%2B1%29%5E2 - pi%2Ar%5E2 = 5
pi%2A%28r%5E2%2B2r%2B1%29 - pi%2Ar%5E2 = 5
Divide both sides by pi
%28r%5E2%2B2r%2B1%29 - r%5E2 = 5%2Fpi
2r + 1 = 1.59
2r = 1.59 - 1
2r = .59
r = .59%2F2
r = .295 m is the radius of the smaller, 1.295 m is the radius of the larger
:
:
Check this on a calc: enter (pi*1.295^2) - (pi*.295^2) = 4.995 ~ 5