Find the minimum cost of a can.

In the classic problem of minimizing the surface area of a cylinder or minimizing the cost of constructing a can subject to a constraint such as fixed volume, students sometimes have a tough time visualizing cylinders of varying heights and radii and imagining that they all can have exactly the same volume.  This GeoGebra worksheet enables the student to explore the dynamic relationship between the cost and the dimensions of a can.  Also, by adjusting the unit cost of the top and bottom of the can independently of the unit cost of the lateral side, students can see the dynamic effect on the cost function, its minimum value, and the resulting dimensions of the can of minimum cost.