The amount of material required is proportional to theOriginally Posted by Vigo
surface area of the cylinder. This is:
that is the area of the curved part of the can, plus the area of the
two end pieces.
The volume of the cylinder is:
Where is the radius of the base, and is the height of
That the volume is fixed allows you to write as a function
of by rearranging the second of these equations. Substituting
this for in the first equation gives you the surface area
as a function of and .
You then need to find the minimum of by
differentiating w.r.t. , and setting the derivative
equal to .