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Say the radius of the circle is x. This makes the area of the circle pi x2. Since the length of the square's sides is the diameter of the circle, 2x, its area is 2x * 2x = 4x2. The percentage occupied by the circle is the area of the circle divided by the area of the square times 100 pi/4 x 100; pi/4 x 100 = 100pi/4 = 25pi = 78.6%.

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Q: What percentage of the square is occupied by the circle when it is inscribed in a square and tangent at all four sides?
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