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

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Math Expert
Joined: 02 Sep 2009
Posts: 50730
In the figure above, the two axes divide the enclosed region into four  [#permalink]

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13 Dec 2017, 19:57
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:40) correct 32% (01:35) wrong based on 58 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 602 times ]

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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, 22:03
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, 22:03
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