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# If the four identical smaller circles in the figure above each have a

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Math Expert
Joined: 02 Sep 2009
Posts: 51035
If the four identical smaller circles in the figure above each have a  [#permalink]

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23 Aug 2018, 02:17
00:00

Difficulty:

15% (low)

Question Stats:

92% (01:32) correct 8% (01:09) wrong based on 26 sessions

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If the four identical smaller circles in the figure above each have a circumference of $$2\pi$$, and the area of the outer circle is 6 times the area of a smaller circle, what is the area of the shaded region?

A. $$\pi$$

B. $$2\pi$$

C. $$3\pi$$

D. $$4\pi$$

E. $$5\pi$$

Attachment:

image013.jpg [ 5.38 KiB | Viewed 282 times ]

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Re: If the four identical smaller circles in the figure above each have a  [#permalink]

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23 Aug 2018, 03:39
Bunuel wrote:

If the four identical smaller circles in the figure above each have a circumference of $$2\pi$$, and the area of the outer circle is 6 times the area of a smaller circle, what is the area of the shaded region?

A. $$\pi$$

B. $$2\pi$$

C. $$3\pi$$

D. $$4\pi$$

E. $$5\pi$$
Attachment:
image013.jpg

r=radius of small circle, R=Radius of outer circle
Circumference of each identical smaller circle=$$2\pi$$
or, $$2\pi$$r=$$2\pi$$
Or, r=1
area of the outer circle is 6 times the area of a smaller circle.
Or, $$\pi*R^2=6*\pi*r^2=6*\pi$$

Area of shaded portion=Area of outer circle-4* Area of one smaller circle=$$\pi*R^2-4\pi*r^2=6*\pi-4\pi=2\pi$$

Ans. (B)
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Re: If the four identical smaller circles in the figure above each have a &nbs [#permalink] 23 Aug 2018, 03:39
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# If the four identical smaller circles in the figure above each have a

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