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# There are two co-centric circles of unequal diameters. The area betwee

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
There are two co-centric circles of unequal diameters. The area betwee  [#permalink]

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05 Oct 2018, 00:38
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Difficulty:

15% (low)

Question Stats:

95% (01:41) correct 5% (01:55) wrong based on 30 sessions

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There are two co-centric circles of unequal diameters. The area between the circles is shaded. If the area of the shaded region is 3 times the area of the smaller circle, then the circumference of the larger circle is how many times the circumference of the smaller circle?

(A) 3
(B) 2.5
(C) 2
(D) √3
(E) √2

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Joined: 29 Jan 2017
Posts: 6
Re: There are two co-centric circles of unequal diameters. The area betwee  [#permalink]

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05 Oct 2018, 03:44
Radius of larger circle(R2) will be twice that of smaller circle(R1). Hence the circumference will be twice that of smaller circle. Answer is C

$$\pi$$ ($$R2^{2}$$ -$$R1^{2}$$)=3$$\pi$$
solving this we get, R2=2R1

Circumference of larger circle=2$$\pi$$R2=2$$\pi$$(2R1)=2(2$$\pi$$R1)=2*Circumference of smaller circle
Math Expert
Joined: 02 Aug 2009
Posts: 7957
Re: There are two co-centric circles of unequal diameters. The area betwee  [#permalink]

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05 Oct 2018, 03:47
Bunuel wrote:
There are two co-centric circles of unequal diameters. The area between the circles is shaded. If the area of the shaded region is 3 times the area of the smaller circle, then the circumference of the larger circle is how many times the circumference of the smaller circle?

(A) 3
(B) 2.5
(C) 2
(D) √3
(E) √2

The shaded area is 3 times the area of inner circle..
So area of outer circle =4*area of inner circle....
$$π*(r_l)^2=4*π*(r_s)^2.......r_l=2r_s........2πr_l=2*(2πr_s).....\frac{2πr_l}{2πr_s}$$=2

C
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Re: There are two co-centric circles of unequal diameters. The area betwee   [#permalink] 05 Oct 2018, 03:47
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