L7.8 - Arcs and Sectors
Learning Intentions and Success Criteria
- Generalize (orally and in writing) methods for calculating lengths of arcs and areas of sectors in circles.
- Calculate lengths of arcs and areas of sectors in circles.
8.1: Math Talk: Fractions of a Circle
8.2: Sector Areas and Arc Lengths
For each circle, find the area of the shaded sector and the length of the arc that outlines the sector. All units are centimeters. Give your answers in terms of 𝜋.
A
B
C
8.3: Build a Method
Mai says, “I know how to find the area of a sector or the length of an arc for central angles like 180 degrees or 90 degrees. But I don’t know how to do it for central angles that make up more complicated fractions of the circle.” 1. In the diagram, the sector’s central angle measures degrees and the circle’s radius is r units. Use the diagram to tell Mai how to find the area of a sector and the length of an arc for any angle and radius measure.
2. This image shows a circle with radius and central angle measurements. Find the area of the shaded sector, and the length of the arc defined by the sector.
Lesson Synthesis: Arcs and Sectors
1. Compare and contrast the processes for finding the area of a sector and calculating the length of an arc. 2. What are some examples in the real world of arcs or sectors?
Show the calculations to get these answers. 3. Arc length: 3𝜋 cm
4. Sector area: 6𝜋 cm2
5. Show the arc length and sector area.
Learning Intentions and Success Criteria
- Generalize (orally and in writing) methods for calculating lengths of arcs and areas of sectors in circles.
- Calculate lengths of arcs and areas of sectors in circles.
Cool-down: Use Your Method
1. Find the area of the shaded sector.
2. Find the length of the arc defined by the sector.
