SOLUTION: The area of a circular ring is 90. If the radius of the outer circle forming the ring is 10, what is the radius of the inner circle of the ring? (assuming the circles forming the r

Algebra ->  Circles -> SOLUTION: The area of a circular ring is 90. If the radius of the outer circle forming the ring is 10, what is the radius of the inner circle of the ring? (assuming the circles forming the r      Log On


   

Question 210713: The area of a circular ring is 90. If the radius of the outer circle forming the ring is 10, what is the radius of the inner circle of the ring? (assuming the circles forming the ring have the same center.)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a circular ring is 90.
If the radius of the outer circle forming the ring is 10, what is the radius of
the inner circle of the ring? (assuming the circles forming the ring have the same center.)
:
Let r = radius of the inner circle
:
The equation:
Large circle area - inner circle = 90
pi%2A10%5E2 - pi%2Ar%5E2 = 90
pi%2A100 - pi%2Ar%5E2 = 90
divide the equation by pi
100 - r^2 = 90%2Fpi
100 - r^2 = 28.648
100 - 28.648 = r^2
r^2 = 71.352
r = sqrt%2871.352%29
r = 8.447 is the radius of the inner circle
:
:
Check solution
pi%2A10%5E2 - pi%2A8.447%5E2
100*pi - 71.352*pi =
314.16 - 224.16 = 90