
If you have access to The Geometer's Sketchpad software, the following sketches can be used to illustrate the shape of the paper and the resulting shapes of the graphs of surface area and volume. If you don't have access to GSP, you can still download the graphs and view them using the demo version of the software. Demo versions for both Windows and Mac are available from Key Curriculum Press.
Paper with Constant AreaThis sketch shows a draggable piece of paper with a constant area (93.5 in^{2}). It then graphs the height of the paper versus the volume and the length of the paper versus the volume. Either graph can be shown separately.
Click on the graph to download the sketch.
Paper with Constant PerimeterThis sketch shows a draggable piece of paper with a constant perimeter (39 in). It then graphs the width of the paper versus both surface area and volume.
Click on the graph to download the sketch. 
