Volume of the cylindrical can.

Formula for the volume of cylinder is , where is radius and is height.

.

(a)

Find the cost function in terms of .

Cost = top + bottom + side.

Area of the top and bottom .

Area of the side .

Substitute .

.

Cost of the top and bottom = 6(area of the top and bottom)

                                       .

Cost of the side = 4(area of the side)

                      .

.

(b)

Graph the function .

Identify the minimum point of the graph.

Graph of the function :

Observe the graph:

The minimum point occurs at .

Therefore, the cost is smallest when .

(a) .

(b) The cost is smallest when .