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There is a circle inscribed in a square, shown on the above figure. If

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There is a circle inscribed in a square, shown on the above figure. If the length of the square is 2, what is the area of one of the 4 regions shaded?

A. \(1-π\)
B. \(2-π\)
C. \(4-π\)
D. \(1-(\frac{π}{2})\)
E. \(1-(\frac{π}{4})\)
[Reveal] Spoiler: OA

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Re: There is a circle inscribed in a square, shown on the above figure. If [#permalink]

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New post 23 Feb 2017, 20:38
MathRevolution wrote:
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1.png


There is a circle inscribed in a square, shown on the above figure. If the length of the square is 2, what is the area of one of the 4 regions shaded?

A. \(1-π\)
B. \(2-π\)
C. \(4-π\)
D. \(1-(\frac{π}{2})\)
E. \(1-(\frac{π}{4})\)


area of one of the 4 regions shaded = (area of Square - area of circle)/4
= (4-pi)/4 = 1- pi/4

Hence Option E is correct
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Re: There is a circle inscribed in a square, shown on the above figure. If [#permalink]

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New post 26 Feb 2017, 21:28
==> The area of the square-area of the \(circle=2^2- π=4- π\), and since it asks for one of the 4 regions shaded, you get \(\frac{4- π}{4}=1-(\frac{π}{4})\).

The answer is E.
Answer: E
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Re: There is a circle inscribed in a square, shown on the above figure. If [#permalink]

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New post 08 Mar 2017, 22:13
Silly mistake- but fixed it- you have to multiply 1 by 1 to get the area of one fourth of the square and then subtract it by the area of the remaining portion of the circle inside it; though, you can just find the area of the circle and divide it by 4. Thus,

1 x 1= 1
pi (1)^2= pi (1) / 4

1- pi(1)/4
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Re: There is a circle inscribed in a square, shown on the above figure. If [#permalink]

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New post 09 Mar 2017, 01:20
Side of square = diameter of circle = 2 x radius\therefore radius = diameter/2 = 1

Area of shaded region = area of square - area of circle = 2 x2 - pi*1*1 = 4 -pi

Since there are 4 equal parts of the shaded region, area of one shaded region = (4 -pi)/4 = 1 - pi/4

Option E

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Re: There is a circle inscribed in a square, shown on the above figure. If [#permalink]

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New post 29 Jan 2018, 20:23
Can someone please explain to me why the area of the circle isnt pi*radius^2? Why is it just pi?
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Re: There is a circle inscribed in a square, shown on the above figure. If [#permalink]

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New post 29 Jan 2018, 21:04
teamryan15 wrote:
Can someone please explain to me why the area of the circle isnt pi*radius^2? Why is it just pi?



The area is \(pi*r^2\) itself but the length of square is 2, which is equal to diameter. Hence radius is 2/2=1
So r^2=1^2=1..
What is left is pi*r^2=pi*1^2=pi
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Re: There is a circle inscribed in a square, shown on the above figure. If   [#permalink] 29 Jan 2018, 21:04
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