Find the ratio of the area inside the square but ouside the circle, to the area of the square in picture?

Question

the picture looks like a square and a circle is inside of it. Also, the picture shows a line passing through half of the circle which is being called r. For radius.

Answer 1

the ratio = 1 - pir^2/(2r)^2 = 1 - pi/4

Answer 2

Ratio = (Area(square) - Area(circle) )/ Area(square)

Area(square) = s^2 where s = square side
Area(circle) = pi*r^2

How do you find s? Look at the triangle formed by the diameter (of length 2r) of the circle and two sides of the square. Two sides of the triangle have length s; the other has length 2r. It is a RIGHT TRIANGLE, so it's angles are 45 degrees, 45 degrees, and 90 degrees. You know the length of the side opposite the 90 degree angle is 2r. Based on the triginometry of 45-45-90 triangles, which you can see here: http://regentsprep.org/regents/mathb/5B1/Tri45.htm, you know that if 2r = sqrt(2), s = 1 = sqrt(2) / sqrt(2) = 2r /sqrt(2)

Therefore, the area of the square is s^2 = 4r^2 / 2

Answer 3

OK, you want the difference between the area of a square with 1 side = 2r and a circle of radius r.
So the square: area = side^2 = 4 r^2
For the circle: area = pi r^2
Ratio = (4-pi)/4

Answer 4

r=2423523.242