SOLUTION: A circle with radius of square root of 2 units is circumscribed about a square with side length 2 units. Find the probability that a randomly chosen point will be inside the circle

Question 37051This question is from textbook Geometry-reasoning applying measuring
: A circle with radius of square root of 2 units is circumscribed about a square with side length 2 units. Find the probability that a randomly chosen point will be inside the circle but outside the square This question is from textbook Geometry-reasoning applying measuring

Found 2 solutions by stanbon, cleomenius:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A circle with radius of square root of 2 units is circumscribed about a square with side length 2 units. Find the probability that a randomly chosen point will be inside the circle but outside the square
Draw the picture of the square inside the circle.
Area of the circle is (pi)(sqrt2)^2=2pi
Area of square is 2^2=4
Area in the circle but not in the square = 2pi-4
Probability of a point being in the circle but not
in the square = (2pi-4)/2pi = (pi - 2)/pi = 1-2/pi
Cheers,
Stan H.
Answer by cleomenius(959) (Show Source): You can put this solution on YOUR website!
I did this problem the following way:
The area of the circle is pi * Square root of 2 squared, or 2; = 6.24.
The area of the square is 2*2 or 4
So, 6.24 - 4 will be the area of the outside the square, but inside the circle. (2.24)
divide this by the area of the circle (6.24), this should give you the probability
2.24 / 6.24 = 0.36 probability.
Cleomenius.
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