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?