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12 Jul 2020, 06:07
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B
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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
A. π/6
B. π/4
C. π/2
D. π/√2
E. π
yashikaaggarwal
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12 Jul 2020, 06:18
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Diagonal of square = 2√2
Hence Side of square = 2 (Diagonal^2 = 2*Side^2)
Area of square = 4
Side of square= diameter of circle.
Area of circle = πr^2
=> π*1*1 => π
the probability that the point lies inside the circle = Area of circle/Area of square
=> π/4
Answer is B
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Hence Side of square = 2 (Diagonal^2 = 2*Side^2)
Area of square = 4
Side of square= diameter of circle.
Area of circle = πr^2
=> π*1*1 => π
the probability that the point lies inside the circle = Area of circle/Area of square
=> π/4
Answer is B
Posted from my mobile device
12 Jul 2020, 07:43
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QuantMadeEasy
If a circle is inscribed in a square then
Side of Square = Diameter of circle
DIagonal of square = Side*√2 = 2√2
i.e. Side of Square = Diameter of Circle = 2/2 = 1
Now, Required Probability \(= \frac{Area of Circle }{ Area of Sqaure} = \frac{πr^2 }{ side^2} = \frac{π1^2}{2^2} = \frac{π}{4}\)
Answer: Option B
