SOLUTION: Two concentric circles are drawn so that the shaded area is equal to the unshaded area. The radius of the outer circle is 8 cm. Find the difference in the radii of the two circles.

Algebra ->  Circles -> SOLUTION: Two concentric circles are drawn so that the shaded area is equal to the unshaded area. The radius of the outer circle is 8 cm. Find the difference in the radii of the two circles.      Log On


   

Question 1208982: Two concentric circles are drawn so that the shaded area is equal to the unshaded area. The radius of the outer circle is 8 cm. Find the difference in the radii of the two circles.
Answer by ikleyn(52781) About Me  (Show Source):
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Two concentric circles are drawn so that the shaded area is equal to the unshaded area.
The radius of the outer circle is 8 cm. Find the difference in the radii of the two circles.
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outer circle   inner circle   shaded/unshaded
  area            area           area
 
pi%2A8%5E2        - pi%2Ar%5E2      =   pi%2Ar%5E2.


From this equation

    8%5E2 = r%5E2 + r%5E2,

    64 = 2r%5E2,

    r%5E2 = 64/2 = 32,

    r = sqrt%2832%29 = 4%2Asqrt%282%29


The difference in the radii is  8+-+4%2Asqrt%282%29 = 2.343146  cm  (rounded).     ANSWER

Solved.