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A square has sides of length 10, and a circle centered at one of its

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A square has sides of length 10, and a circle centered at one of its  [#permalink]

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New post 21 Mar 2019, 23:21
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Question Stats:

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A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the circle?


(A) \(200 + 25\pi\)

(B) \(100 + 75\pi\)

(C) \(75 + 100\pi\)

(D) \(100 + 100\pi\)

(E) \(100 + 125\pi\)

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Re: A square has sides of length 10, and a circle centered at one of its  [#permalink]

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New post 22 Mar 2019, 00:06
Bunuel wrote:
A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the circle?


(A) \(200 + 25\pi\)

(B) \(100 + 75\pi\)

(C) \(75 + 100\pi\)

(D) \(100 + 100\pi\)

(E) \(100 + 125\pi\)



IMO B

We have find the area of region in attached image

which is equal = area of square + 3/4( area of circle )



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Re: A square has sides of length 10, and a circle centered at one of its  [#permalink]

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New post 22 Mar 2019, 02:18
Bunuel wrote:
A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the circle?


(A) \(200 + 25\pi\)

(B) \(100 + 75\pi\)

(C) \(75 + 100\pi\)

(D) \(100 + 100\pi\)

(E) \(100 + 125\pi\)


area of circle = 100pi
and area of square = 100
about 3/4 of circle is inside square we need to find overlap area of both
so
3/4 * 100pi + 100 = 75pi + 100
IMO B
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Re: A square has sides of length 10, and a circle centered at one of its   [#permalink] 22 Mar 2019, 02:18
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