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Math Help - rectangle cut from circle - maxima problem

  1. #1
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    rectangle cut from circle - maxima problem

    A rectangle is cut from a circular disc of radius 6 cm. Find the area of the largest rectangle that can be produced
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by differentiate View Post
    A rectangle is cut from a circular disc of radius 6 cm. Find the area of the largest rectangle that can be produced
    The diagonal of the rectangle is the diameter of the circle.

    Let x be the width, y the height.

    You want to maximize the function xy given that \sqrt{x^2+y^2}=12\implies x^2+y^2=144.
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    Thanks. I got the answer. its 72
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    Super Member redsoxfan325's Avatar
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    That looks right. Notice that it's a square. This will often be the case when you want to maximize area (or volume).
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