Concept Topic GuideCBSE & ICSEClass 10MathematicsAreas Related to CirclesVerified Faculty Notes & Solutions
Areas Related to Circles – Class 10 Maths Chapter 11: Sector, Segment & Formulas
Class 10 Areas Related to Circles: circumference, area, sector, segment, combined figure problems with formulas for CBSE & ICSE boards.
5 students readUpdated 4 September 2026
Chapter 11: Areas Related to Circles
11.1 Basic Formulas
Circumference of circle = 2πr
Area of circle = πr²
Where r = radius. Use π = 22/7 or 3.14 as specified.
Area of circle = πr²
Where r = radius. Use π = 22/7 or 3.14 as specified.
11.2 Sector of a Circle
A sector is the region enclosed between two radii and the corresponding arc.
Length of arc = (θ/360°) × 2πr
Area of sector = (θ/360°) × πr²
Where θ is the angle of the sector at the centre.
Area of sector = (θ/360°) × πr²
Where θ is the angle of the sector at the centre.
11.3 Segment of a Circle
A segment is the region between a chord and the corresponding arc.
Area of minor segment = Area of sector − Area of triangle
Area of major segment = Area of circle − Area of minor segment
Area of major segment = Area of circle − Area of minor segment
11.4 Solved Examples
Example 1: Find the area of a sector of a circle with radius 6 cm if the angle of the sector is 60°.
Solution
Area = (60/360) × π × 6² = (1/6) × 22/7 × 36 = 132/7 = 18.86 cm²
Example 2: A chord subtends an angle of 90° at the centre of a circle of radius 14 cm. Find the area of the minor segment.
Solution
Area of sector = (90/360) × (22/7) × 14² = (1/4) × (22/7) × 196 = 154 cm²
Area of triangle = (1/2) × 14 × 14 = 98 cm²
Area of minor segment = 154 − 98 = 56 cm²
Board Exam Tip — Shaded Region Problems:
Many exam questions ask for the area of a "shaded region" formed by combinations of circles, semicircles, and quadrants.
Strategy: Area of shaded region = Area of larger figure − Area of unshaded parts (or sum of simpler areas that make up the shaded region).
Many exam questions ask for the area of a "shaded region" formed by combinations of circles, semicircles, and quadrants.
Strategy: Area of shaded region = Area of larger figure − Area of unshaded parts (or sum of simpler areas that make up the shaded region).
Indexed Topics & Examination Keywords
#areas related to circles class 10#sector area#segment area#arc length#circumference#NCERT maths#CBSE#ICSE#shaded region
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