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In the figure above, each of the 4 equal circles touch the square at

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In the figure above, each of the 4 equal circles touch the square at  [#permalink]

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New post 14 Sep 2018, 02:13
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In the figure above, each of the 4 equal circles touch the square at exactly 2 points. If each circle touches exactly 2 other circles at one point and has a radius of 4, what is the area of the shaded region?


A. 192 – 48π
B. 192 – 60π
C. 240 – 68π
D. 240 – 60π
E. 256 – 64π


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Re: In the figure above, each of the 4 equal circles touch the square at  [#permalink]

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New post 16 Sep 2018, 10:19
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Area of the shaded portion as marked in above figure \(= 4^2 - \frac{90}{360}* \pi * 4^2 = 16 - 4 \pi\)

There are 12 such shaded areas in the figure.

Total Shaded area \(= 12*(16 - 4 \pi) = 192-48 \pi\)
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In the figure above, each of the 4 equal circles touch the square at  [#permalink]

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New post 16 Sep 2018, 11:00
Area of square = (4 x radius of circle) = 16^ = 256
If you join the center of the circles , you get a smaller square with side = 8. Area = 64
You lose 1/4th of each circle. Area of remaining circle = 3/4 (because you lost 1/4th) * 4 (there are 4 circles) * π * r^2 = 48π
Area of shaded region = 256-64-48π = 192-48π
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In the figure above, each of the 4 equal circles touch the square at   [#permalink] 16 Sep 2018, 11:00
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In the figure above, each of the 4 equal circles touch the square at

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