Question

Problem: a circle is inscribed in a square. The squares perimeter is 16 times the square root of 6. What is the probability of selecting a point that is outside the circle??

•please explain and show steps in detail on how to solve for the correct answer

Answer 1

I got 21% at selecting a point outside.
Explanation: Since the perimeter is 16sqrt (6), each side must be 4sqrt (6)
This also means that the diameter is 4sqrt (6).

To find the area of a circle, we need to find the radius (2sqrt (6)).
Area of circle is pi × (2sqrt (6))^2 = 24pi or approximately 75.4 units^2
Area of square is 4sqrt (6)^2 = 96

Thus, let's take the area of the circle and subtract that from the area of our square to yield approx. 20.6 units^2
and now divide through by 96 to yield 21%