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As the figure above shows, four identical circles are inscri

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As the figure above shows, four identical circles are inscri [#permalink] New post 17 Feb 2011, 14:04
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185. As the figure above shows, four identical circles are inscribed in a square. If the distance between centers of circle A and В is 4sq2 , what is the area of the shaded region?
(A) 256 – 72п
(B) 256 – 64п
(C) 256 – 32п
(D) 128 – 32п
(E) 64 – 16п
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Re: As the figure above shows, four identical circles are inscri [#permalink] New post 17 Feb 2011, 14:19
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banksy wrote:
185. As the figure above shows, four identical circles are inscribed in a square. If the distance between centers of circle A and В is 4sq2 , what is the area of the shaded region?
(A) 256 – 72п
(B) 256 – 64п
(C) 256 – 32п
(D) 128 – 32п
(E) 64 – 16п
Attachment:
untitled.PNG
untitled.PNG [ 2.74 KiB | Viewed 1933 times ]
As you can see on the diagram above AB is the hypotenuse of the isosceles right triangle with legs equal to 2r (45-45-90 right triangle --> ratio of the sides 1:1:\sqrt{2}). Now, as AB=hypotenuse=4\sqrt{2} then 2r=leg=\frac{4\sqrt{2}}{\sqrt{2}}=4 --> r=2.

Shades region = are of the square - area of the circles = (4r)^2-4*\pi{r^2}=64-16\pi.

Answer: E.
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Re: As the figure above shows, four identical circles are inscri [#permalink] New post 19 Apr 2011, 18:36
AB = 4root(2)

So The diameter of circle = 4

Area of aquare = 4+4 = 8

Area of shaded part = 64 - 4*pi*4 = 64 - 16pi

Answer - E
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Re: As the figure above shows, four identical circles are inscri [#permalink] New post 19 Apr 2011, 19:04
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Distance AB = 4sq2
So each side of triangle = 4
Radius of circle = 2
Each side of Square = 8

Area of shaded portion = area of square - area of 4 circles
= (8*8) - 4*pi(2)square
= 64 - 16 pi

Correct Answer E
Re: As the figure above shows, four identical circles are inscri   [#permalink] 19 Apr 2011, 19:04
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