Area of Circle Question

[PeterRobinson44]

A circle of radius 1 is inscribed in a square with side length 2. If 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?



Is the formula no matter the radius or the side always. A = (pi * r^2) / 4?

I know the answer to this particular problem is pi/4 * 1000 = 785. However, I want to make sure that the formula no matter the side or radius is correct. Thank you for any help.

 

[Dr.Peterson]

A circle of radius 1 is inscribed in a square with side length 2. If 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?

Is the formula no matter the radius or the side always. A = (pi * r^2) / 4?

I know the answer to this particular problem is pi/4 * 1000 = 785. However, I want to make sure that the formula no matter the side or radius is correct. Thank you for any help.

Well, if the radius doesn't matter, why is there an r in your formula?

The probability of being in the circle is the ratio of areas, [pi r^2]/(2r)^2, since the side length is twice the radius. This simplifies to pi/4, which hopefully is what you intended, which leads to the answer you gave (no matter what the radius is).