A complicated mathematical modeling problem in senior high school

Another angle of this problem is actually how to maximize the area in length. Let the radius be r, the width of the rectangle be a, and the area be s, then s = π r 2+a * 2r, 2r * 2+2a = l；; S = π r 2+(L-4R) R = (π-4) R 2+LR. According to the parabola method, the maximum value of S is r=L/(8-2π).

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