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Each circle has center O. The radius of the smaller circle i
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13 Jun 2018, 22:09
13 Jun 2018, 22:09
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Question Stats:
71% (00:57) correct
28% (01:17) wrong based on 7 sessions
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Each circle has center O. The radius of the smaller circle is 2 and the radius of the larger circle is 6. If a point is selected at random from the larger circular region, what is the probability that the point will lie in the shaded region?
A. \(\frac{1}{9}\)
B. \(\frac{1}{6}\)
C. \(\frac{2}{3}\)
D. \(\frac{5}{6}\)
E. \(\frac{8}{9}\)
Re: Each circle has center O. The radius of the smaller circle i
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13 Jun 2018, 22:19
13 Jun 2018, 22:19
1
amorphous wrote:
Each circle has center O. The radius of the smaller circle is 2 and the radius of the larger circle is 6. If a point is selected at random from the larger circular region, what is the probability that the point will lie in the shaded region?
A. \(\frac{1}{9}\)
B. \(\frac{1}{6}\)
C. \(\frac{2}{3}\)
D. \(\frac{5}{6}\)
E. \(\frac{8}{9}\)
A. \(\frac{1}{9}\)
B. \(\frac{1}{6}\)
C. \(\frac{2}{3}\)
D. \(\frac{5}{6}\)
E. \(\frac{8}{9}\)
Total area of larger circle is 36*pi.
Area of smaller circle is 4*pi.
Now To get the area of shaded part ,we need to separate total area - smaller area = 32pi ( 36pi - 4pi).
Now to get the probability for the shaded part we need to take entire area of the maximum circle in the denominator.
Since p(a) = expected records / Total records.
i.e shaded / full circle => 32pi / 36pi => 8/9.
E.
gmatclubot
Re: Each circle has center O. The radius of the smaller circle i [#permalink]
13 Jun 2018, 22:19
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