SOLUTION: Two concentric circles are drawn so that the inner circle is shaded. The shaded area is equal to the unshaded area. The radius of the outer circle is 12 cm. Find the difference in

Algebra ->  Circles -> SOLUTION: Two concentric circles are drawn so that the inner circle is shaded. The shaded area is equal to the unshaded area. The radius of the outer circle is 12 cm. Find the difference in       Log On


   

Question 1101875: Two concentric circles are drawn so that the inner circle is shaded. The shaded area is equal to the unshaded area. The radius of the outer circle is 12 cm. Find the difference in the radii of the two circles.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Just in all variables:
R, radius of outer, larger circle
r, radius of inner, shaded circle

The larger circle would be TWICE the area of the shaded smaller circle.
pi%2AR%5E2-pi%2Ar%5E2=pi%2Ar%5E2
pi%2AR%5E2=pi%2Ar%5E2%2Bpi%2Ar%5E2
pi%2AR%5E2=2%2Api%2Ar%5E2

2r%5E2=R%5E2
r%5E2=%281%2F2%29R%5E2
r=R%2Fsqrt%282%29 or highlight%28r=%28sqrt%282%29%2F2%29R%29

You can substitute for R to finish.