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A circle is inscribed in a square with diagonal length 2√2
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12 Jul 2020, 05:09
12 Jul 2020, 05:09
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Question Stats:
71% (00:56) correct
28% (01:04) wrong based on 32 sessions
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A circle is inscribed in a square with diagonal length 2√2. A point is randomly chosen inside the square. What is the probability that the point lies inside the circle?
A. π/6
B. π/4
C. π/2
D. π/√2
E. π
My channel URL: https://www.youtube.com/channel/UCvdY0k ... EOsT5PMFRQ
A. π/6
B. π/4
C. π/2
D. π/√2
E. π
My channel URL: https://www.youtube.com/channel/UCvdY0k ... EOsT5PMFRQ
Re: A circle is inscribed in a square with diagonal length 2√2
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12 Jul 2020, 09:57
12 Jul 2020, 09:57
1
Step 1: Understanding the question
When the side of the square is a, length of its diagonal = a√2 = 2√2
Therefore, a =2.
As the circle is inscribed in the circle, its diameter is equal to the side of the square. Hence, diameter = 2, radius =1
Step 2: Calculation
We know, probability = \(\frac{No. Of desired outcome}{Total No of outcomes}\)
Total number of outcomes = area of the square = \(a^2\) = 4
No of desired outcomes = area of the circle = \(π(1)^2\) = π
Required Probability = \(\frac{π}{4}\)
(B) is correct
Channel URL for your self study: https://www.youtube.com/channel/UCvdY0k ... EOsT5PMFRQ
When the side of the square is a, length of its diagonal = a√2 = 2√2
Therefore, a =2.
As the circle is inscribed in the circle, its diameter is equal to the side of the square. Hence, diameter = 2, radius =1
Step 2: Calculation
We know, probability = \(\frac{No. Of desired outcome}{Total No of outcomes}\)
Total number of outcomes = area of the square = \(a^2\) = 4
No of desired outcomes = area of the circle = \(π(1)^2\) = π
Required Probability = \(\frac{π}{4}\)
(B) is correct
Channel URL for your self study: https://www.youtube.com/channel/UCvdY0k ... EOsT5PMFRQ
gmatclubot
Re: A circle is inscribed in a square with diagonal length 2√2 [#permalink]
12 Jul 2020, 09:57
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