You also need to know that the area of the top and bottom, each, is and the area of the curved side is the area of the rectangle having width equal to the height of the can, h, and length equal to thecircumferenceof the circular base (imagine cutting the curved side of the can down its length and flattening it), and so is . Multiply each of those three areas by its cost and add to find the total cost in terms of thetwovariables, r and h.

Since , you can solve that for either r in terms of h or h in terms of r. In the equation for cost, replace, in (a), h by its formula in terms of r and, in (b), r by its formula in terms of h.