This key facts covers Key Formulas 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 2 of 5 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Key Formulas
| Arc Length | (θ/360) × πd or (θ/360) × 2πr |
| Sector Area | (θ/360) × πr² |
| Fraction of Circle | θ/360 (where θ is the angle) |
| Perimeter of Sector | Arc length + 2 × radius |
Practice questions for Sectors & Arcs
What is the correct formula for the arc length of a sector with radius r and angle θ (in degrees)?
Explain how the arc length and sector area formulae are derived from the formulae for the full circle.
Quick recall flashcards
Sector Area
Area = (θ/360) × πr² for angle θ
Arc Length
Arc = (θ/360) × πd for angle θ