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In the figure shown, if the area of the shaded region is 3

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In the figure shown, if the area of the shaded region is 3 [#permalink] New post 04 Feb 2006, 16:52
In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?
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 [#permalink] New post 04 Feb 2006, 16:56
Two times?

Smaller circle = pi*r^2
Larger circle = pi*R^2

Given ,

pi*R^2 - pi*r^2 = 3* pi*r^2

R^2 = 4*pi*r^2

R = 2*r

Ratio of circimference = 2*pi*R/2*pi*r = 2
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 [#permalink] New post 04 Feb 2006, 17:32
Agree with Giddi's working :wink:
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 [#permalink] New post 04 Feb 2006, 17:43
I think it should be 1+ sqrt3 or 1 - sqrt3

Area of the shaded region is : Pi(R-r)^2 = 3 Pi r^2
(R-r)^2 = 3r^2
R-r =rsqrt3
or
R-r = -rsqrt3

If i See the options available for the PS, I might be able to answer it..

OA?
  [#permalink] 04 Feb 2006, 17:43
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In the figure shown, if the area of the shaded region is 3

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