Circles

Lesson 13

Math

Unit 7

10th Grade

Lesson 13 of 14

Objective


Calculate the sector area of a circle. Identify relationships between sector area, arc angle, and radius.

Common Core Standards


Core Standards

  • G.C.B.5 — Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Foundational Standards

  • 7.G.B.4

Criteria for Success


  1. Given the central angle and radius, calculate the sector area of a circle.
  2. Describe the relationship of the sector area with the radius and with the arc length.
  3. Find the central angle measure of a sector given the radius and sector area. 
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Anchor Problems

25-30 minutes


Problem 1

What is the area of the shaded region shown below where circle $$A$$ has a radius of $$\overline{AB}$$ measuring $$4$$ units?

Guiding Questions

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Problem 2

If you would like to eat the most pizza, which coupon should you use?

Guiding Questions

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References

Dan Meyer's Three-Act Math Pizza DoublerAct One

Pizza Doubler by Dan Meyer is licensed under the CC BY 3.0 license. Accessed June 13, 2017, 12:16 p.m..

Target Task

5-10 minutes


Circle $$A$$ and circle $$C$$ are shown below. 

  1. How many times greater is the area of the shaded sector shown in circle $$A$$ than in circle $$C$$? How does this compare to the ratio of the radii?
  2. What is the difference in sector areas? 

References

GeoGebra Geometry - 8.13 TT

Geometry - 8.13 TT by Match Fishtank is made available by GeoGebra under the CC BY-NC-SA 3.0 license. Copyright © International GeoGebra Institute, 2013. Accessed June 13, 2017, 12:24 p.m..

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where students are given the area of a circle and central angle and asked to find the sector area.
  • Include problems where students are given the sector area and central angle and asked to find the radius or arc length.

Next

Use sector area of circles to calculate the composite area of figures.

Lesson 14
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Equations of Circles

Topic B: Angle and Segment Relationships in Inscribed and Circumscribed Figures

Topic C: Arc Length, Radians, and Sector Area

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