SOLUTION: I have 2 drawings. One has a circle inscribed in a square(round peg in square hole). The other has a square inscribed in a circle.(square peg in round hole)How do I determine which

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Question 187055: I have 2 drawings. One has a circle inscribed in a square(round peg in square hole). The other has a square inscribed in a circle.(square peg in round hole)How do I determine which one is the better fit? Is there some method to this madness????
Found 2 solutions by vleith, stanbon:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
I would try to find out which of those two options ends up with the ratio of the areas of the two figures being closest to 1.
For the circle inside the square, let the square have a side of 1. Then the circle has a diameter of 1. Now find the ratio of the area of the circle to the area of the square. (littler area over the larger area).
Then do the same for the square inside the circle. Let the side of the square be 1. In this case the diameter of the circle is sqrt(2). Now find the ratio of squareArea/circleArea.
The ratio that is closest to '1' is the set that 'fits better' IMHO

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
One has a circle inscribed in a square(round peg in square hole). The other has a square inscribed in a circle.(square peg in round hole)How do I determine which one is the better fit? Is there some method to this madness????
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The better fit is the one where the inner figure fills more of the
area of the outer figure.
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If the circle is inside the square:
Area of the square = s^2
Area of the circle = (pi)(s/2)^2 = (1/4)pi*s^2 = 0.7854*s^2
The area of the square that remains is (1-0.7854)s^2 = 0.2146s^2
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If the square is inside the circle:
Comment:
Now you need to know if the two circles are of the same size
of if the two squares are of the same size, because you need
to relate the two figures.
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Cheers,
Stan H.