Use circular base area for cylinder volume and capacity
Use the radius rather than diameter in πr²h · Distinguish total height from filled depth · Convert internal volume to litres
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
- Circle area
- Prism volume and capacity units
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
- Use the radius rather than diameter in πr²h
- Distinguish total height from filled depth
- Convert internal volume to litres
A circular constant section
A right circular cylinder has volume πr²h, where h is perpendicular to its circular base. Diameter d gives radius d/2. For radius 3 cm and height 8 cm, volume is 72π cm³. Doubling radius alone multiplies volume by four; doubling height alone multiplies it by two.
Internal capacity
For a container, use internal radius and depth to calculate capacity; external dimensions include wall thickness. A partial fill uses the actual liquid depth, not the total container height. With centimetre dimensions, the result is in cm³ or ml, then divide by 1000 for litres.
Sources for this lesson
Pause and explain
If cylinder diameter is 6 cm, what radius belongs in its volume formula?
Worked example
Find the volume of a radius-3 cm cylinder of height 8 cm.
Show the worked solution
- Base area=π×3²=9π cm².
- Volume=9π×8=72π cm³.
Answer 72π cm³.
Try a topic test
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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.
Find the volume of a cylinder with radius 2 cm and height 5 cm.
Give me a hint
Multiply circular area by height.
Compare my reasoning
- Base area=4π cm².
- Volume=4π×5=20π cm³.
20π cm³.
Look for these in your work
- Use radius
- Retain exact pi
A cylinder has diameter 10 cm and height 12 cm. Find its volume.
Give me a hint
First find radius 5 cm.
Compare my reasoning
- Base area=25π cm².
- Volume=25π×12=300π cm³.
300π cm³.
Look for these in your work
- Convert diameter correctly
- Use cubic units
A tank has internal radius 3 cm and total height 10 cm. Water depth is 7 cm. Find the water volume in cm³ and litres.
Give me a hint
Use the filled depth only.
Compare my reasoning
- Volume=π×3²×7=63π cm³.
- Litres=63π/1000=0.063π litres ≈ 0.198 litres to 3 significant figures.
63π cm³; 0.063π litres ≈ 0.198 litres.
Look for these in your work
- Use internal filled dimensions
- Convert after calculating
Common mistakes
- Halve the diameter before squaring.
- Use the depth of the filled part.
What can you explain now?
If cylinder diameter is 6 cm, what radius belongs in its volume formula?
Compare with the explanation
3 cm.
The radius is half the diameter.
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Make it stick
If cylinder diameter is 6 cm, what radius belongs in its volume formula?
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.