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Calculating Arcs and Areas of Sectors of Circles

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Calculating Arcs and Areas of Sectors of Circles

 
This lesson unit is intended to help you assess how well students are able to solve problems involving area and arc length of a sector of a circle using radians. It assumes familiarity with radians and should not be treated as an introduction to the topic. This lesson is intended to help you identify and assist students who have difficulties in:
Computing perimeters, areas, and arc lengths of sectors using formulas.
Finding the relationships between arc lengths, and areas of sectors after scaling.

Lucky Cow

Resource:
Lucky Cow

3 Acts activity about the area of a sector.

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Orbiting Satellite

Resource:
Orbiting Satellite

This task provides a context for connecting an angle in radians to the arc length intercepted by the angle. 

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Setting Up Sprinklers

Resource:
Setting Up Sprinklers

This task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7). 

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