Knowledge Organiser: Sectors & Arcs
Key Terms
- Sector: A "pizza slice" region bounded by two radii and an arc
- Arc: A curved portion of the circumference
- Angle θ: The angle at the centre of the sector (in degrees)
- Minor sector: The smaller sector (angle < 180°)
- Major sector: The larger sector (angle > 180°)
Must-Know Facts
- Both formulas use the fraction θ/360 of the full circle
- Perimeter of sector = arc length + 2 × radius
- A semicircle is a sector with θ = 180°
- A quarter circle is a sector with θ = 90°
- Leave answers as multiples of π when asked
Key Formulas
- Arc length: L = (θ/360) × 2πr
- Sector area: A = (θ/360) × πr²
- Sector perimeter: P = L + 2r
Common Mistakes
- Sector perimeter: P = arc length + 2r (two radii): don't just give the arc length
- Using diameter instead of radius: If a question gives the diameter, halve it first to get the radius (r = d ÷ 2)
- Angle in degrees: θ/360 is the fraction: make sure angle is in degrees, not a fraction already
- Exact vs decimal answers: Leave in terms of π when asked for exact answers
Worked Examples
Find the area of a sector with radius 6cm and angle 60°. Step 1 Find the fraction Fraction = 60/360 = 1/6 Step 2 Calculate area Area = (1/6) × π × 6² = (1/6) × 36π = 6π = 18.85 cm² (2 d.p.)