Chapter 37: Area of Sectors of a Circle: Situation 31 From the MACMTL–CPTM Situations Project

An honors geometry class had the following problem for homework.

Complete the following (see Figure 37.1) for a circle with radius 3:

A student asked simply, “How do you do this?”

What could this problem afford beyond a series of simple calculations? If the question is passed off as simply a chance to practice computations, then perhaps something is missed. The problem could have been chosen to provide an opportunity to use a spreadsheet, write a program for a handheld calculator, or to look for patterns in the completed table. The completed table could suggest exploring a graph of the five number pairs. This Prompt allows for the introduction of radian measure as a more efficient representation of the sector's area formula. Students can also explore possible values for the area using both the table and programming features of a graphing calculator. In addition, a spreadsheet can be useful in calculating the area. Such uses of technology support students as they attempt to find values within the domain and range of the continuous function represented by the formula. All of these are means to explore the underlying functional relationship of sector areas and their central angles.