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pow:problem1f20

Problem 1 (suggested by Prof. Matt Brin) (due Monday, September 14)

A loop of string has fixed length $L$. It is looped around a disk of radius $r$ and pulled tight at one point so as to form an “ice cream cone” shape as pictured here. Consider the region labeled $A$ that is inside the loop of string, but outside the disk. Note that the area of $A$ is zero if either $r=0$ or if $r=L/2\pi$. What value of $r$ maximizes the area of the region $A$ and what is this maximum value of the area?

This was our warm-up problem but only two solutions were received, from John Giaccio and Yuqiao Huang, both correct. Both solutions are similar to the solution discussed in the following link Solution