Calculate circumference and area from the correct radius
Convert diameter to radius before finding area · Keep circumference and area distinct · Use exact pi expressions before requested rounding
Section Paper 1 · Historical Core · non-calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Powers and square roots
- Circle radius and diameter
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Convert diameter to radius before finding area
- Keep circumference and area distinct
- Use exact pi expressions before requested rounding
One circle, two measurements
A circle of radius r has circumference 2πr = πd and area πr², where d=2r. A circumference is a boundary length; area measures its enclosed region. If a diameter is given, halve it before squaring for area.
Calculate and reverse
For diameter 10 cm, r=5 cm, circumference 10π cm and area 25π cm². If circumference is known, r=C/(2π). If area is known, r=√(A/π), taking the non-negative length. Keep π until the final rounding step; follow any value of π supplied by a task.
Sources for this lesson
Pause and explain
What is the area of a circle with diameter 10 cm?
Worked example
A circle has diameter 10 cm. Find exact circumference and area.
Show the worked solution
- Radius is 5 cm.
- C=2π×5 and A=π×5².
Answer 10π cm; 25π cm².
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A circle has radius 4 m. Find exact circumference and area.
Give me a hint
Use separate formulae.
Compare my reasoning
- C=2π×4 = 8π m.
- A=π×4² = 16π m².
8π m; 16π m².
Look for these in your work
- Select the requested measurement
- Retain exact pi
A circle has circumference 18π cm. Find radius and area.
Give me a hint
Divide the circumference by 2π.
Compare my reasoning
- r=18π/(2π)=9 cm.
- A=π×9² = 81π cm².
Radius 9 cm; area 81π cm².
Look for these in your work
- Reverse the boundary formula
- Then calculate area
A circular garden has diameter 12 m. Compare fencing around it with turf for its interior. Give exact amounts and approximations to 3 significant figures.
Give me a hint
Use radius 6 m.
Compare my reasoning
- Fencing length is 12π m ≈ 37.7 m.
- Turf area is 36π m² ≈ 113 m².
Fencing 12π m ≈ 37.7 m; turf 36π m² ≈ 113 m².
Look for these in your work
- Use the correct units
- Round only the final values
Common mistakes
- Squaring a diameter instead of a radius makes area four times too large.
- Rounding π early can alter the final answer.
What can you explain now?
What is the area of a circle with diameter 10 cm?
Compare with the explanation
25π cm².
Halve the diameter to get radius 5 cm, then calculate π×5²=25π cm².
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Make it stick
What is the area of a circle with diameter 10 cm?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.