Geometry & MeasuresTopic Summary
Knowledge Organiser: Circumference & Area of Circles
Part of Circumference & Area of Circles · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Circumference & Area of Circles within Circumference & Area of Circles for GCSE Mathematics. Revise Circumference & Area of Circles in Geometry & Measures for GCSE Mathematics with 11 exam-style questions and 7 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 10 of 10 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 10 of 10
Practice
11 questions
Recall
7 flashcards
Knowledge Organiser: Circumference & Area of Circles
Key Terms
- Radius (r): Distance from centre to edge
- Diameter (d): Distance across through centre; d = 2r
- Circumference: Perimeter of a circle
- Pi (π): ≈ 3.14159… — use the π button on your calculator
- Annulus: Region between two concentric circles
Must-Know Facts
- Circumference uses LINEAR units (cm, m) — NOT squared
- Area uses SQUARE units (cm², m²)
- If given diameter, halve it to get radius BEFORE using A = πr²
- If radius increases by k%, circumference increases by k% but area increases by more
- Leave answers as multiples of π when the question asks (e.g. 25π cm²)
- Annulus area = π(R² − r²)
Key Formulas
- Circumference: C = πd = 2πr
- Area: A = πr²
- Radius from C: r = C ÷ (2π)
- Radius from A: r = √(A ÷ π)
Common Mistakes
- Using diameter instead of radius: Area = πr² uses RADIUS — if given diameter, halve it first
- Circumference with r²: C = 2πr (not 2πr²) — circumference is linear, area is squared
- Semicircle area: A = ½πr² — remember to halve the full circle area
- Leaving answer as decimal not exact: If the question says "give your answer in terms of π", leave as e.g. 25π cm²