We set the perimeter of the base of the proposed cone (2 Pi R) equal to the available perimeter of the wire formed sector (2 Pi - theta)r.

Input := 


ConeBase = 2 Pi R == (2 Pi - theta) r/.solr[[1]]

Output =


          L (2 Pi - theta)

2 Pi R == ----------------

          2 + 2 Pi - theta