Since the students will be worried about this, explain that some physicists created the drums and tested them in real life. Students can cut one of the drums into pieces and try to fit the pieces onto the other drum. They will discover that the drums do not have the same area, which contradicts the fact that they must in order to sound the same. Students can resolve the apparent conflict by investigating the accuracy of the models. Students can identify which drum resembles the drum that Carolyn is holding in Figure 1.
Student can cut along their folds and then try to fit the pieces onto the other drum.
Once they identify which piece does not fit properly, they can compare an uncut version of the drum to Carolyn's drum in Figure 1 in order to see that this piece was not drawn to scale. Explain the dangers of relying on models by discussing some of the difficulties involved in creating physical models representing abstract figures with precisely determined sides. Challenge the students to create a perfect model of Carolyn's drum that is drawn to the same scale as the other drum. Using Geometer's Sketchpad While many of the ideas that we describe here can be nicely visualized in a dynamic geometry software program such as Geometer's Sketchpad, problems arise with accuracy. Then, students can use the Measure command to have the program calculate the area and perimeter of each figure.