Geometry & MeasuresTopic Summary
Knowledge Organiser: Sectors & Arcs
Part of Sectors & Arcs · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Sectors & Arcs within Sectors & Arcs for GCSE Mathematics. Revise Sectors & Arcs in Geometry & Measures for GCSE Mathematics with 10 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 5
Practice
10 questions
Recall
3 flashcards
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: All sector/arc formulas use r, not d
- 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