The amount of material required is proportional to theOriginally Posted byVigo

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

the can.

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 .

RonL