Areas Related to Circles — Notes
📑 Chapter Navigator
01
11.1 Sector and Segment
A sector is the region bounded by two radii and the corresponding arc. A segment is the region between a chord and its corresponding arc.
02
11.2 Area of a Sector
For central angle θ in degrees and radius r:
Area of sector = (θ/360°)πr2.
Area of sector = (θ/360°)πr2.
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11.3 Length of an Arc
The length of an arc subtending θ at the centre is:
Arc length = (θ/360°)·2πr.
Arc length = (θ/360°)·2πr.
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11.4 Area of a Segment
Area of minor segment = area of sector − area of corresponding triangle. For a major segment, use the whole circle appropriately.
05
11.5 Composite Figures
For paths, shaded regions and combined shapes, split the figure into familiar regions such as circles, sectors, triangles and rectangles. Add or subtract their areas according to the diagram.
⚡ Quick Revision
- Sector area = θ/360 × πr².
- Arc length = θ/360 × 2πr.
- Segment = sector − triangle for the minor segment.
- Use π consistently, usually 22/7 or 3.14 as instructed.
🎯 Board Exam Focus
- Check whether θ is the minor or major angle.
- Write units as cm²/m² for area and cm/m for length.
- Sketch the subtraction in composite-region questions.
🚀 Last-Minute Revision
✔ Read every formula with its conditions and symbols.
✔ Write given data first and keep units consistent.
✔ For proofs, state the theorem and show logical steps.
✔ Check signs, substitutions and final units.
❤️ Examisthan.com • Class 10 CBSE Mathematics • Chapter 11: Areas Related to Circles