If you measure a typical can you will find it has the same height as diameter across. Why is this so? Let us suppose that the can has to contain a certain fixed volume. Let us also assume that the shape is going to be cylindrical: such a shape is easy to produce in manufacture. But such a cylinder might be long and thin, or it might be short and broad. The manufacturer will try to choose dimensions which minimize the amount of metal used to produce the can. That is we require a minimal surface area for the can (curved surface plus ends). We need some calculus to show that this occurs when the diameter and height of the can are equal.
