CBSE Class 10 Maths: Areas Related to Circles — Notes 2026

Circle Basics Recap

• Area of circle = πr²; Circumference = 2πr; use π = 22/7 or 3.14 as specified in question
• Diameter = 2r; area in terms of diameter: πd²/4; circumference = πd
• CBSE: if not specified, use π = 22/7; otherwise use value given

Area and Perimeter of Sector

• Sector: pie-slice shaped region; area = (θ/360°) × πr²; arc length = (θ/360°) × 2πr
• Perimeter of sector = 2r + arc length (two radii + arc)
• Example: sector of radius 14 cm with angle 90°: area = (90/360) × 22/7 × 196 = 154 cm²

Area of Segment

• Minor segment = area of sector − area of triangle OAB (formed by two radii and chord)
• Triangle OAB area: for θ = 90°, it is r²/2; for θ = 60°, it is (√3/4)r²
• Major segment = area of circle − area of minor segment

Combination of Figures

• Track around oval: area = area of big rectangle − area of small rectangle + 2 semicircles
• Shaded region problems: area of outer figure − area of inner figure; or add specific parts
• Typical CBSE: square with inscribed circle; find area of shaded region (corner pieces)

Flower/Petal Patterns

• Four quarter-circles inside a square of side a: each petal area = (area of quarter circle − area of triangle) × 2
• Common CBSE question: 4 equal circles in a square; find area enclosed between circles (shaded region)
• Area of each circle = π(a/2)²; area of 4 circles combined − area of square = overlap regions

Unit Conversion

• Area: cm² to m² (÷ 10000); m² to km² (÷ 1,000,000); acres, hectares in application problems
• Cost problems: cost of fencing perimeter = perimeter × rate; cost of carpeting area = area × rate/m²
• Rate in ₹ per m²: common in CBSE application questions

CBSE Board Exam Tips

• Areas Related to Circles: 3–6 marks; combination figure problems most common in 3-mark questions
• Show formula, substitution, and simplified answer clearly; π value must be consistent throughout
• Segment area question: draw sector and triangle separately; calculate each area; subtract