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In the figure above, the two axes divide the enclosed region into four

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Joined: 02 Sep 2009
Posts: 47898
In the figure above, the two axes divide the enclosed region into four  [#permalink]

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13 Dec 2017, 20:57
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Difficulty:

35% (medium)

Question Stats:

58% (01:04) correct 42% (00:42) wrong based on 52 sessions

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In the figure above, the two axes divide the enclosed region into four regions that have the same size and shape. Of the following, which is closest to the area of the entire enclosed region?

(A) 7
(B) 10
(C) 19
(D) 22
(E) 29

Attachment:

2017-12-12_2124_001.png [ 42.26 KiB | Viewed 539 times ]

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Joined: 14 Oct 2015
Posts: 252
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In the figure above, the two axes divide the enclosed region into four  [#permalink]

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13 Dec 2017, 23:03
Bunuel wrote:

In the figure above, the two axes divide the enclosed region into four regions that have the same size and shape. Of the following, which is closest to the area of the entire enclosed region?

(A) 7
(B) 10
(C) 19
(D) 22
(E) 29

Attachment:
2017-12-12_2124_001.png

It should be D

A quick glance reveals the square region is $$4x4$$ (area $$16$$) and is domed by four semicircles of radius $$1$$. These semicircles add up to make $$2$$ circles of radius $$1$$ with an area of $$(πr^2 + πr^2) = 2π= 6.28$$. Total area would be a little over $$16+2π$$ or just over $$22$$.
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In the figure above, the two axes divide the enclosed region into four &nbs [#permalink] 13 Dec 2017, 23:03
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