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In the figure above, if the square inscribed in the circle h

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In the figure above, if the square inscribed in the circle h [#permalink] New post 04 Jun 2016, 07:12
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#GREpracticequestion In the figure above, if the square inscribed in the circle.jpg
#GREpracticequestion In the figure above, if the square inscribed in the circle.jpg [ 11.95 KiB | Viewed 8671 times ]


In the figure above, if the square inscribed in the circle has an area of 16, what is the area of the shaded region?

A. \(2\pi – 1\)

B. \(2\pi – 4\)

C. \(4\pi – 2\)

D. \(4\pi – 4\)

E. \(8\pi – 4\)


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[Reveal] Spoiler: OA

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Re: In the figure above, if the square inscribed in the circle h [#permalink] New post 04 Jun 2016, 07:21
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Explanation

Attachment:
#GREpracticequestion In the figure above, if the square inscribed in the circle.jpg
#GREpracticequestion In the figure above, if the square inscribed in the circle.jpg [ 16.38 KiB | Viewed 6669 times ]


If the area of the square is 16, that means each side is 4-

Now we do have an isosceles triangle with two equal side

\(x:x:x\sqrt{2}\)

\(4 : 4 : 4 \sqrt{2}\)

So the side of the triangle which is also the circumference. Therefore, the radius is half that \(\frac{4 \sqrt{2}}{2} = 2 \sqrt{2}\) and the area of the circle is \(\pi r^2=\pi(2 \sqrt{2} )^2 = 8 \pi\)

The area we are looking for is \(\frac{8\pi - 16}{4} = 2\pi - 4\)

B is correct
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Re: In the figure above, if the square inscribed in the circle h [#permalink] New post 05 Aug 2019, 08:16
Can you explain further detail for the steps after finding 8π? I understand the values but I don't understand why.
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Re: In the figure above, if the square inscribed in the circle h [#permalink] New post 05 Aug 2019, 08:56
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ehilario wrote:
Can you explain further detail for the steps after finding 8π? I understand the values but I don't understand why.

8π is the area of the circle
Since the area of the square (that's inside the circle) is 16, then 8π - 16 represents the area of ALL 4 tiny circle pieces.
Since we just want the area of ONE tiny circle piece, we need to divide 8π - 16 by 4

Does that help?

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Re: In the figure above, if the square inscribed in the circle h [#permalink] New post 05 Aug 2019, 09:43
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Yes it does, thank you!

GreenlightTestPrep wrote:
ehilario wrote:
Can you explain further detail for the steps after finding 8π? I understand the values but I don't understand why.

8π is the area of the circle
Since the area of the square (that's inside the circle) is 16, then 8π - 16 represents the area of ALL 4 tiny circle pieces.
Since we just want the area of ONE tiny circle piece, we need to divide 8π - 16 by 4

Does that help?

Cheers,
Brent
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Re: In the figure above, if the square inscribed in the circle h [#permalink] New post 07 Oct 2020, 00:09
sandy wrote:
Explanation

Attachment:
#GREpracticequestion In the figure above, if the square inscribed in the circle.jpg




If the area of the square is 16, that means each side is 4-

Now we do have an isosceles triangle with two equal side

\(x:x:x\sqrt{2}\)

\(4 : 4 : 4 \sqrt{2}\)

So the side of the triangle which is also the circumference. Therefore, the radius is half that \(\frac{4 \sqrt{2}}{2} = 2 \sqrt{2}\) and the area of the circle is \(\pi r^2=\pi(2 \sqrt{2} )^2 = 8 \pi\)

The area we are looking for is \(\frac{8\pi - 16}{4} = 2\pi - 4\)

B is correct


can you explain why you divide 8π - 16 with 4?
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Re: In the figure above, if the square inscribed in the circle h [#permalink] New post 07 Oct 2020, 05:24
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sleepyowl wrote:
sandy wrote:
Explanation

Attachment:
#GREpracticequestion In the figure above, if the square inscribed in the circle.jpg




If the area of the square is 16, that means each side is 4-

Now we do have an isosceles triangle with two equal side

\(x:x:x\sqrt{2}\)

\(4 : 4 : 4 \sqrt{2}\)

So the side of the triangle which is also the circumference. Therefore, the radius is half that \(\frac{4 \sqrt{2}}{2} = 2 \sqrt{2}\) and the area of the circle is \(\pi r^2=\pi(2 \sqrt{2} )^2 = 8 \pi\)

The area we are looking for is \(\frac{8\pi - 16}{4} = 2\pi - 4\)

B is correct


can you explain why you divide 8π - 16 with 4?


The area of the circle is 8π
The area of the inscribed Square is 16
So, 8π - 16 = the area of the FOUR partial circles (one of which is shaded)
So to find the area of the ONE shaded partial circle, we must divide by 4
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Re: In the figure above, if the square inscribed in the circle h   [#permalink] 07 Oct 2020, 05:24
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