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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
Joined: 16 Aug 2015
Posts: 8001
GMAT 1: 760 Q51 V42
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Seven small circles of radius 2 are cut from the large circle, as show  [#permalink]

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14 Dec 2018, 00:57
00:00

Difficulty:

5% (low)

Question Stats:

96% (01:22) correct 4% (00:48) wrong based on 39 sessions

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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 [ 14.11 KiB | Viewed 327 times ]

$$A. 8π$$
$$B. 20π$$
$$C. 32π$$
$$D. 48π$$
$$E. 64π$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 09 Jun 2014 Posts: 352 Location: India Concentration: General Management, Operations Re: Seven small circles of radius 2 are cut from the large circle, as show [#permalink] ### Show Tags 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 Joined: 16 Aug 2015 Posts: 8001 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Seven small circles of radius 2 are cut from the large circle, as show [#permalink] ### Show Tags 16 Dec 2018, 18:40 => Attachment: 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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