Convert cubic units and liquid capacity consistently
Cube a length conversion factor for volume · Connect cubic centimetres with millilitres · Convert between litres, centilitres and cubic metres
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
- Metric lengths and powers
- Cuboid volume
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
- Cube a length conversion factor for volume
- Connect cubic centimetres with millilitres
- Convert between litres, centilitres and cubic metres
Three dimensions
A 1 cm cube has edges of 10 mm, so its volume is 10³ = 1000 mm³. A 1 m cube has edges of 100 cm, so 1 m³ = 1 000 000 cm³. The exponent follows the measured dimension: length uses one factor, area its square, volume its cube.
Capacity and volume
1 cm³ = 1 ml, 1 litre = 1000 ml = 1000 cm³, 1 cl = 10 ml, and 1 m³ = 1000 litres. These equalities convert volume or capacity. Converting a volume into a mass requires an additional density assumption; a litre is not always a kilogram.
Sources for this lesson
Pause and explain
What is 1 cm³ in mm³?
Worked example
Convert 0.025 m³ to litres and millilitres.
Show the worked solution
- 0.025×1000 = 25 litres.
- 25×1000 = 25 000 ml.
Answer 25 litres; 25 000 ml.
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.
Convert 4 cm³ to mm³.
Give me a hint
Cube the factor of 10.
Compare my reasoning
- 1 cm³ = 1000 mm³.
- 4×1000 = 4000 mm³.
4000 mm³.
Look for these in your work
- Use three dimensions
- Retain cubic units
Convert 35 cl to ml and litres.
Give me a hint
1 cl is 10 ml.
Compare my reasoning
- 35×10 = 350 ml.
- 350÷1000 = 0.35 litres.
350 ml; 0.35 litres.
Look for these in your work
- Keep capacity factors distinct
- Cross-check the quantities
A cuboid tank has internal dimensions 40 cm by 25 cm by 30 cm. Find its capacity in litres; can its full contents be assigned a mass without knowing the liquid?
Give me a hint
Find the internal volume first.
Compare my reasoning
- Volume = 40×25×30 = 30 000 cm³ = 30 litres.
- Mass also depends on the liquid density, which is not supplied.
30 litres; the mass cannot be determined from volume alone.
Look for these in your work
- Use internal dimensions
- Identify missing information
Common mistakes
- Do not reuse an area conversion for volume.
- Volume alone does not determine mass.
What can you explain now?
What is 1 cm³ in mm³?
Compare with the explanation
1000 mm³.
All three edges contribute the factor of 10.
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Make it stick
What is 1 cm³ in mm³?
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.