The U.S. Postal Service will only mail packages that meet certain size requirements. For cylinder-shaped packages (or "rolls"), the minimum length is 4 inches and the maximum length is 36 inches. There is also a restriction that the length plus two diameters can be no more than 42 inches (why do you think they have this restriction?).
What are the dimensions of an acceptable cylinder-shaped package that will have the greatest volume?
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Cube / Rectangular Prism Activity
Activity to get students to think about the linear measurements and the corresponding area and volume measurements of the cube and the rectangular prism.
Submit your idea for an investigation to InterMath.