Problem: Maximum Volume of a Cone
A circular disc of radius R is used to make a Cone
by removing a sector with angle ø and then joining the
edges where the sector was removed. What is the maximum volume
that such a cone can attain? That is, what angle ø for
a disc of radius R would you remove to make a cone of maximum
volume?
In this illustration the sector of the circular disc is removed
and the edges joined to form the cone as shown below where r is
the radius of the base of the cone. The circumference of the base
of the cone is 
