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# In the diagram above, B is the center of the larger circle. AB is the

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
In the diagram above, B is the center of the larger circle. AB is the  [#permalink]

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28 Jan 2019, 02:23
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Difficulty:

25% (medium)

Question Stats:

71% (01:12) correct 29% (01:07) wrong based on 62 sessions

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In the diagram above, B is the center of the larger circle. AB is the radius of the larger circle and the diameter of the smaller circle. The shaded area is what fraction of the larger circle?

A. 1/8
B. 1/4
C. 1/2
D. 2/3
E. 3/4

Attachment:

GRE exam - In the diagram above, B is the center of the larger circle. .jpg [ 12.44 KiB | Viewed 703 times ]

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In the diagram above, B is the center of the larger circle. AB is the  [#permalink]

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28 Jan 2019, 02:33
AB is the diameter of the smaller circle.
Area = $$\frac{π*AB^2}{4}$$

The radius of bigger circle = AB
Area of the bigger circle = $$π*AB^2$$
Area of the shaded portion = Area of the bigger circle - Area of the smaller circle
$$π*AB^2$$ - $$\frac{π*AB^2}{4}$$
$$\frac{3AB^2}{4}$$ = Shaded area

Now,
$$\frac{3πAB^2}{4}$$/$$πAB^2$$ = 3/4

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Re: In the diagram above, B is the center of the larger circle. AB is the  [#permalink]

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28 Jan 2019, 04:09
Bunuel wrote:

In the diagram above, B is the center of the larger circle. AB is the radius of the larger circle and the diameter of the smaller circle. The shaded area is what fraction of the larger circle?

A. 1/8
B. 1/4
C. 1/2
D. 2/3
E. 3/4

Attachment:
GRE exam - In the diagram above, B is the center of the larger circle. .jpg

let AB = 4
so area of larger circle ; 16pi
and small circle ; 4pi
shaded area = 16-4 = 12 pi
ratio
12pi/16pi ; 3/4
IMO E
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Posts: 4018
Re: In the diagram above, B is the center of the larger circle. AB is the  [#permalink]

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03 May 2019, 06:26
Top Contributor
Bunuel wrote:

In the diagram above, B is the center of the larger circle. AB is the radius of the larger circle and the diameter of the smaller circle. The shaded area is what fraction of the larger circle?

A. 1/8
B. 1/4
C. 1/2
D. 2/3
E. 3/4

Attachment:
GRE exam - In the diagram above, B is the center of the larger circle. .jpg

Let r = radius of SMALLER circle
So, 2r = radius of LARGER circle (since the diameter of the SMALLER circle = radius of LARGER circle)

Area of SMALLER circle = πr²
Area of LARGER circle = π(2r)² = π4r²

Area of shaded part = area of LARGER circle - area of SMALLER circle
= π4r² - πr²
= π(4r² - r²)
= π3r²

The shaded area is what fraction of the larger circle?
Faction = π3r²/π4r² = 3/4

Cheers,
Brent
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Re: In the diagram above, B is the center of the larger circle. AB is the   [#permalink] 03 May 2019, 06:26
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