Chapter 11 — Areas Related to Circles

NCERT Class 10 Maths Chapter 11 covers areas related to circles, teaching students how to calculate the area and arc length of a sector using the formula (θ/360) × πr², and the area of a segment by subtracting the corresponding triangle area from the sector area.

Chapter 11 of NCERT Class 10 Mathematics focuses on Areas Related to Circles. It introduces key concepts of sectors and segments of a circle. A sector is the region enclosed by two radii and the corresponding arc, while a segment is the region between a chord and its arc. Using the unitary method, the chapter derives that the area of a sector with radius r and central angle θ is (θ/360) × πr², and the arc length is (θ/360) × 2πr. The area of a segment equals the area of the corresponding sector minus the area of the triangle formed by the two radii and the chord.

1. 01A sector is the region enclosed by two radii and an arc; a segment is the region between a chord and its arc — both come in minor and major variants.
2. 02Area of a sector with radius r and central angle θ (in degrees) = (θ/360) × πr².
3. 03Length of an arc of a sector with radius r and angle θ = (θ/360) × 2πr.
4. 04Area of a segment = Area of the corresponding sector − Area of the corresponding triangle (formed by the two radii and the chord).
5. 05Area of the major sector = πr² − Area of the minor sector; area of the major segment = πr² − Area of the minor segment.
6. 06The unitary method underlies all sector and arc-length formulas: the full circle (360°) has area πr², so a θ° sector has area proportional to θ/360.