ISSUES RELATED TO THE PROBLEM
This problem is an extension on the older problem of cutting out a sector from a fixed radius circle such that when the two edges of the sector are attached a cone of maximum volume will be formed.
In this problem apparently there are two variables - the radius of the region and the angle of the sector. However, the student should be able to eliminate one of these variables by using the total length of the wire as a constraint and thus create a function of one variable to optimize.