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
Worked Examples
A circle has diameter 14 cm. Find its circumference. Give your answer to 1 decimal place. Step 1 Write the formula C = πd Step 2 Substitute the values C = π × 14 Step 3 Calculate C = 43.98... = 44.0 cm (1 dp)
Worked Examples
A circle has radius 5 cm. Find its area. Give your answer to 1 decimal place. Step 1 Write the formula A = πr² Step 2 Square the radius first r² = 5² = 25 Step 3 Multiply by π A = π × 25 = 78.539... = 78.5 cm² (1 dp)