Read and see

URL http://math.rice.edu/~lanius/Geom/cyls.htmlThe ProblemTake a sheet of paper, and roll it up to form a baseless cylinder. Now take another sheet, rotate the paper, and form another baseless cylinder. Think about the volume of each cylinder and make a prediction.

A Prediction

- Would the two volumes be equal?
- Would the short cylinder have greater volume?
- Would the tall cylinder have greater volume?

ExplanationWhy did you predict as you did?

A DemonstrationTape two sheets of paper to form the two cylinders, one short and one tall (Stiff paper is helpful. I use transparency sheets). Hold the tall cylinder upright in a shallow box and fill with rice. Now fill the shorter cylinder, and compare the two amounts of rice. Was your prediction correct?

The CalculationCalculate both volumes. (You may need these formulas)

- Circumference = 2(pi)(r)
- Volume = (pi)(r^2)h

V=

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Copyright 1998-2008 Cynthia Lanius