Crossroads in Mathematics

Example 3

Tennis Ball Can (Measurement and Geometry Formula)

"Clearly" the height of a can of three tennis balls is greater than the circumference of the can. Or is that really the case? The following problem can be used to compare results obtained by measurement to results obtained by using a geometric formula. Groups of students should be given a common tennis ball can along with two paper tapes, one calibrated in inches (to eighths or sixteenths) and the other in centimeters (to tenths).

Problem. Which is greater, the height of the cylindrical tennis ball can or its circumference? By how much?

a. Estimate the answer by simple observation.

b. Measure the height and the diameter of the can. Determine the circumference using a geometric formula. Compare the height to the circumference.

c. Measure the circumference of the can with a paper tape measure. How does the measurement compare with the results obtained from the geometric formula? Compare the height to the circumference.

Notice that the problem does not indicate which paper tape to use for the measurements and the level of precision needed in the answers. At the conclusion of the exercise, faculty should lead students to discuss the merits of the U.S. customary system and the metric system. Furthermore, faculty may also use the example to discuss rounding and the potential errors in the answers. The ideas of precision, accuracy, and rules for operations with numbers that are the results of measurements play a key role in the education of science and technical majors.