STATEMENT OF PROBLEM

Given a 100 cm length of thin wire, make a closed boundary consisting of a circle of radius r with a sector of angle theta cut out of it. We place this closed, planar, wire form in a paper-making, mesh mold. When the two edges of the resulting paper sector from the inner area bounded by the wire are attached there will be formed a cone.

Design the closed boundary so that the paper cone thus formed will have maximum volume.