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Verify this expression computationally using a new copy of Elena’s data with new columns for area of a whole pizza, fraction of a whole pizza, area of a slice, and area per dollar. Demonstrate the process of computing the rst row of the spreadsheet and using the spreadsheet’s auto ll functionality to automatically compute values for each column. Compare these values to those
obtained by using the expression . Tell students that much of the modern economy depends on analyzing and computing in this way, except using spreadsheets that are much, much larger.
Lesson Synthesis
Display an image of a circle with a central angle labeled radians and the radius labeled units.
Arrange students in groups of 2. Ask students to write an expression for the area of the sector in terms of and before sharing their result with their partner. Ask students to share their responses. (
, ) Then ask, “How would your expression change if the angle were a degree measure instead?” ( )
Ask students to add this theorem to their reference charts as you add it to the class reference chart:
Unit 7 Lesson 4: Area of a Sector 43
