The volume of such a can with base radius 
and height 
would be
We desire the base's circumference and the can's height to add to 120, i.e.
Substituting this into
allows us to reduce the volume to a function of a single variable :
Taking the derivative with respect to yields
Set this equal to 0 and find any critical points:
This suggests the can will have maximum volume when its radius is
cm, which would give a volume of about 20,371 sq. cm.
We desire the base's circumference and the can's height to add to 120, i.e.
Substituting this into
Taking the derivative with respect to
Set this equal to 0 and find any critical points:
This suggests the can will have maximum volume when its radius is
