SOLUTION: If a square is drawn inside of a circle such that its four corners are touching the interior edge of the circle, what is the ratio of the area of the square to the area of the circ

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Question 498085: If a square is drawn inside of a circle such that its four corners are touching the interior edge of the circle, what is the ratio of the area of the square to the area of the circle? You should calculate and express your answer as a decimal ratio (i.e. .328 : 1)

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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If a square is drawn inside of a circle such that its four corners are touching the interior edge of the circle, what is the ratio of the area of the square to the area of the circle?
You should calculate and express your answer as a decimal ratio
:
Let s = the side of the square
then
s^2 = area of the square
:
sqrt%282s%5E2%29 = the diagonal of the square, and the diameter of the circle
therefore
sqrt%282s%5E2%29%2F2 = the radius of the circle
:
pi%2A%28sqrt%282s%5E2%29%2F2%29%5E2 = pi%2A%28%282s%5E2%29%2F4%29 = pi%2A%28%28s%5E2%29%2F2%29 = the area of the circle
:
Ratio of the area of the square to the area of the circle
s%5E2%2F%28pi%2A%28s%5E2%2F2%29%29%29 = s%5E2%2A%282%2F%28pi%2As%5E2%29%29%29
Cancel s^2
2%2F%28pi%29 = 1%2F%28pi%2F2%29 = 1:1.5707, square area:circle area