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28 Jan 2019, 02:23
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E
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Difficulty:
25%
(medium)
Question Stats:
73% (01:11) correct
27%
(01:28)
wrong
based on 75
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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 4964 times ]
Chethan92
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28 Jan 2019, 02:33
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AB is the diameter of the smaller circle.
Radius = AB/2
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
E is the answer.
Radius = AB/2
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
E is the answer.
Archit3110
Major Poster
28 Jan 2019, 04:09
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Bunuel
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
