Q1
The area of a sector depends on the:
Aangle and radius
Bradius only
Cangle only
Ddiameter only
CBSEClass 10 (CBSE)MathematicsCh 11 · Topic 1
Area of a Sector and Segment
Learning to calculate the area of a sector and segment of a circle.
Core concept
For example, a sector with radius 7cm and angle 90° has area (90/360) × (22/7) × 7² = (1/4) × 154 = 38.5 cm². To find a minor segment's area (the smaller region cut off by a chord), calculate the sector's area first, then subtract the area of the triangle formed by the two radii and the chord, using either the standard triangle area formula or specific trigonometric formulas when angles are known.
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• Sector area = (θ/360°) x πr², where θ is the central angle.
• A segment is the region between a chord and its arc.
• Segment area = sector area - triangle area (formed by the two radii and the chord).
• Example: sector with radius 7cm, angle 90°, has area 38.5 cm².