Cynthia Lanius
Read and see Encouraging Mathematical Thinking, a videopaper project done with the Math Forum that was based on this problem.(Opens a new window.)

The Problem Take 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?

Explanation Why did you predict as you did?

A Demonstration Tape 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 Calculation Calculate both volumes. (You may need these formulas)

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

	V=
	V=

Next: Volume Functions

Copyright 1998-2008 Cynthia Lanius