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Math Help - Area of Inscribed Figures

  1. #1
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    Area of Inscribed Figures

    Which occupies a larger percentage of the area compared to the figure containing it: a circle inscribed in a square or a square inscribed in a circle? Assume that the inscribed figures are tangent to the outside figures. Explain.
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  2. #2
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    Hi

    The area of a square with length a is A_{square} = a^2

    The diameter of the circle tangent to the square is a. Its area is A_{circle} = \pi\frac{a^2}{4}

    The ratio of the 2 areas is \frac{A_{circle}}{A_{square}} = \frac{\pi}{4} = 78.5 %
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  3. #3
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    Thank you! I had gotten that far as well... I should have specified earlier, I am stuck with the other figure. When you have a square inscribed in a circle, how do you determine the percentage of the circle the square takes up???
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  4. #4
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    The length of the diagonal of the square is a\:\sqrt{2}
    So is the diameter of the large circle
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