📖 Chapter 11 — Areas Related to Circles (CBSE Class 10 Maths): Detailed notes — circumference, area, and the areas of sectors and segments.
Chapter 11 — Areas Related to Circles
⭕ 1. Basic Formulas
Circumference = 2πr · Area of circle = πr² (use π = 22/7 unless stated)
🍕 2. Sector of a Circle (angle θ)
A sector is the region between two radii and the arc.
Length of arc = (θ/360) × 2πr
Area of sector = (θ/360) × πr²
🌙 3. Segment of a Circle
A segment is the region between a chord and its arc.
Area of (minor) segment = Area of sector − Area of triangle formed by the two radii and the chord
🕐 4. Useful Facts
- A quadrant is a sector of angle 90° → area = ¼ πr².
- The minute hand of a clock moves 6° per minute (360° in 60 min).
- For a chord subtending 90° at the centre, the triangle is right-angled with legs = radius.
🧠 Remember: Area of circle = πr², circumference = 2πr. Sector area = (θ/360)πr², arc = (θ/360)·2πr. Segment = sector − triangle. Quadrant = ¼πr². Minute hand → 6° per minute.
⭐ Exam Tips: ① Sector area & arc length. ② Quadrant (90°). ③ Area swept by a clock hand (find the angle first). ④ Area of a segment = sector − triangle. ⑤ Keep π = 22/7 unless told otherwise.