9.8Arc Length and Sector Area
Quick Answer
Arc length = (central angle / 360°) × 2πr. Sector area = (central angle / 360°) × πr². Both formulas use the fraction of the full circle represented by the central angle.
Essential Question
How do arc length and sector area each represent a proportional fraction of the full circle's circumference and area?
Learning Goals
- 1Derive the arc length formula from the circumference formula.
- 2Calculate arc length given radius and central angle.
- 3Derive the sector area formula from the circle area formula.
- 4Calculate sector area given radius and central angle.
- 5Solve problems involving arc length and sector area in context.
Key Vocabulary
Arc length
The distance along an arc; arc length = (θ/360°) × 2πr.
Sector
A region bounded by two radii and their intercepted arc.
Sector area
The area of a sector; sector area = (θ/360°) × πr².
Full lesson content coming soon
Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.