Q1. Find the area of a sector with radius 7 cm and angle 90° (π = 22/7).
Area = (θ/360°) × πr²
Area = (90/360) × (22/7) × 7²
Area = ¼ × 22/7 × 49 = ¼ × 154 = 38.5 cm²
Areas Related to Circles — Class 10
A pizza slice is a sector; the crust-only bit beyond a chord is a segment. Compute both areas — and the arc length — instantly.
SectorThe pie-slice region bounded by two radii and the arc between them.
SegmentThe region between a chord and the arc it cuts off (sector area minus the triangle).
Arc lengthThe length of the curved part of the circle for a given angle θ at the centre.
Sector & arc calculator Interactive
Enter the radius and the angle at the centre to get the arc length and the sector area (π ≈ 3.1416).
Arc length, (θ/360)·2πr—cm
Sector area, (θ/360)·πr²—cm²
A sector with θ = 360° is the whole circle; a sector with θ = 180° is a semicircle.
Numericals practice Interactive
Sector area problems with steps (π = 22/7).
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Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Circumference | C = 2πr |
| Area of circle | A = πr² |
| Arc length | l = (θ/360°) × 2πr |
| Area of sector | A = (θ/360°) × πr² |
| Area of segment | sector area − triangle area |
Common mistakes & exam wins
- A sector with θ = 90° is exactly a quarter of the circle; θ = 180° is a semicircle.
- Segment area = sector area − area of the triangle formed by the two radii and the chord.
- Always keep θ in degrees over 360° in these formulas (unless working in radians).
Frequently asked questions
What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc (a "pie slice"); a segment is bounded by a chord and an arc.
What is the formula for the area of a sector?
Area = (θ/360°) × πr², where θ is the angle at the centre and r the radius.
How do you find the area of a segment?
Subtract the area of the triangle (formed by the two radii and the chord) from the area of the sector.