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Seven small circles of radius 2 are cut from the large circle, as show

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Math Revolution GMAT Instructor
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New post 14 Dec 2018, 00:57
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Question Stats:

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[Math Revolution GMAT math practice question]

Seven small circles of radius 2 are cut from the large circle, as shown. The small circles are tangent each other, and all small circles except for the center circle are tangent to the larger circle. What is the area of the shaded region?

Attachment:
12.14.png
12.14.png [ 14.11 KiB | Viewed 327 times ]


\(A. 8π\)
\(B. 20π\)
\(C. 32π\)
\(D. 48π\)
\(E. 64π\)

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Re: Seven small circles of radius 2 are cut from the large circle, as show  [#permalink]

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New post 14 Dec 2018, 01:07
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Seven small circles of radius 2 are cut from the large circle, as shown. The small circles are tangent each other, and all small circles except for the center circle are tangent to the larger circle. What is the area of the shaded region?

Attachment:
12.14.png


\(A. 8π\)
\(B. 20π\)
\(C. 32π\)
\(D. 48π\)
\(E. 64π\)



So,here is my approach :

Small circle dia = 4 cm
3 small circles make up the larger circle and so dia of larger circle = 12
Hence radius of larger circle = 12/2 = 6 cm

Area of shaded reg= Area of larger circle - Area of 7 smaller circles = pi(6^2 - 7*(2^2)) = 8pi

Hence OA should be A
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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Re: Seven small circles of radius 2 are cut from the large circle, as show  [#permalink]

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New post 16 Dec 2018, 18:40
=>

Attachment:
12.17.png
12.17.png [ 14.96 KiB | Viewed 211 times ]


The radius of the large circle is \(2*2 + 2 = 6.\) Thus, the area of the large circle is \(6^2π = 36π,\) and the area of each of the seven small circles is \(2^2π = 4π.\)
Thus, the area of the shaded region is \(36π – 7(4π) = 8π.\)

Therefore, the answer is A.
Answer: A
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Re: Seven small circles of radius 2 are cut from the large circle, as show   [#permalink] 16 Dec 2018, 18:40
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