Chapter 11: Areas Related to Circles
Mastering the calculations of Sectors, Segments, and Arcs.
🍕 Sector of a Circle
The portion of the circular region enclosed by two radii and the corresponding arc.
Like a slice of pizza! 🍕
Minor Sector (shaded) & Major Sector (unshaded).
🌙 Segment of a Circle
The portion of the circular region enclosed between a chord and the corresponding arc.
Cut by a straight line! 🌙
Minor Segment (shaded) & Major Segment (unshaded).
⚙️ The Master Formulas
Where r is the radius and θ is the angle of the sector in degrees.
Based on total circumference (2πr).
Based on total circle area (πr²).
- Area of ΔOAB
Subtract the triangle from the sector!
⭐ Board Exam Super-Hacks
The Clock Hack ⏰
Questions about minute hands are very common! Remember: The minute hand covers 360° in 60 minutes. Therefore, it sweeps 6° in 1 minute. For 5 minutes, θ = 5 × 6° = 30°.
The Triangle Area Trick
When finding Segment Area, if θ = 60°, the triangle formed is Equilateral (Area = (√3/4)r²). If θ = 90°, it's a Right Triangle (Area = (1/2)r²).
⚠️ Common Exam Traps
Trap 1: Major vs Minor
When a question just says "find the area of the segment/sector", it ALWAYS implies the Minor one unless explicitly stated otherwise. Don't waste time finding both!
Trap 2: Area of Major Sector
To find the Major Sector area, you can either do (πr² - Area of Minor Sector) OR use the formula directly with the reflex angle: [(360° - θ)/360°] × πr².