Area of Sectors
A sector is a “pizza slice” of a circle. Its area is a fraction of the total circle area.
Introduction
Sector = fraction of the circle's area
Past Knowledge
Area of circles (11.2.3). Arc length (11.2.2). Central angles (10.1.2).
Today's Goal
Calculate sector area using the proportion formula.
Future Success
Geometric probability (11.2.5), segment of circle areas.
Key Concepts
Sector Area Formula
Segment of a Circle
The region between a chord and its arc = sector minus the triangle.
Worked Examples
Sector Area
r = 12, θ = 60°.
A = 24π ≈ 75.4
Segment Area
r = 10, θ = 90°. Find the area of the segment.
Sector:
Triangle: (right isosceles)
Segment =
A = 25π − 50 ≈ 28.5
Common Pitfalls
Arc Length vs. Sector Area
Arc length uses ×2πr (circumference). Sector area uses ×πr² (area). Same fraction, different base formula.
Real-Life Applications
Windshield Wipers
A wiper blade sweeps a sector. The wiped area = sector of outer circle minus sector of inner circle.
Radar Scan
A rotating radar beam sweeps a sector every pass. The scanned area per sweep = sector area.
Practice Quiz
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