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

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Math Expert
Joined: 02 Sep 2009
Posts: 59725
A square has sides of length 10, and a circle centered at one of its  [#permalink]

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21 Mar 2019, 23:21
00:00

Difficulty:

55% (hard)

Question Stats:

53% (02:00) correct 47% (02:31) wrong based on 17 sessions

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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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Joined: 25 Feb 2019
Posts: 335
Re: A square has sides of length 10, and a circle centered at one of its  [#permalink]

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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 )

Posted from my mobile device
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IMG_20190322_123508.jpg [ 1.16 MiB | Viewed 319 times ]

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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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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
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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