Metric units, square units and capacity
Convert lengths, masses, areas, volumes and capacities with the correct power of the conversion factor.
Core and Extended.
Before you begin
- Multiply and divide by powers of ten.
- Calculate squares and cubes.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many centimetres equal 1 metre?
What you will learn
- Convert metric length and mass units.
- Square and cube length factors for area and volume.
- Connect cubic centimetres, millilitres, litres and cubic metres.
Identify the quantity before the factor
For length, 1 cm = 10 mm, 1 m = 100 cm and 1 km = 1000 m. For mass, 1 kg = 1000 g. Converting into a smaller unit increases the numerical count; converting into a larger unit decreases it. For example, 2.35 m = 235 cm and 480 g = 0.48 kg.
Area counts squares, so a square of side 1 m contains 100 × 100 centimetre squares: 1 m² = 10 000 cm². Volume counts cubes: 1 m³ = 100³ cm³ = 1 000 000 cm³. Using the single length factor for an area or volume conversion produces a large error even when the decimal movement looks familiar.
Capacity is a volume
One millilitre is one cubic centimetre; 1000 ml = 1 litre. Therefore 1 litre = 1000 cm³ and 1 m³ = 1000 litres. A 0.36 m³ tank holds 360 litres, not 0.36 litres. Keep the equality chain visible when changing both the unit type and its size.
Before combining measurements, convert them to compatible units. A 30 cm by 20 cm by 0.4 m box has height 40 cm, so volume is 24 000 cm³ = 24 litres. Mass cannot be converted to capacity without extra information such as density; 1 kg is not automatically 1 litre for an arbitrary substance.
Pause and explain
Convert 0.025 m² to cm².
Worked example
Convert 0.032 m² to cm² and 0.36 m³ to litres.
Show the worked solution
- The area factor is 100² = 10 000, giving 0.032 × 10 000 = 320 cm².
- One cubic metre is 1000 litres, giving 0.36 × 1000 = 360 litres.
- Check that both smaller-unit numerical counts increased and retain the distinct units.
Answer 320 cm²; 360 litres.
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 3.6 km to metres and 2750 g to kilograms.
Give me a hint
State each unit equality first.
Compare my reasoning
- 1 km = 1000 m, so 3.6 × 1000 = 3600 m.
- 1 kg = 1000 g, so 2750 ÷ 1000 = 2.75 kg.
- The length count increases in smaller units; the mass count decreases in larger units.
3600 m; 2.75 kg.
Look for these in your work
- Used the correct conversion direction.
- Retained length and mass units separately.
Convert 6400 mm² to cm² and 18 000 cm³ to litres.
Give me a hint
Square the 10 mm per cm factor; use 1000 cm³ per litre.
Compare my reasoning
- One cm² is 10² = 100 mm², so 6400/100 = 64 cm².
- 18 000/1000 = 18 litres.
- Check the dimensions before deciding the divisor.
64 cm²; 18 litres.
Look for these in your work
- Squared the length factor.
- Connected cubic volume with capacity.
A tank measures 30 cm by 20 cm by 0.4 m. Find its capacity in litres.
Give me a hint
Use one length unit for all three dimensions.
Compare my reasoning
- Convert 0.4 m to 40 cm.
- Volume is 30 × 20 × 40 = 24 000 cm³.
- Divide by 1000 to obtain 24 litres.
24 litres.
Look for these in your work
- Converted before multiplying.
- Used the cubic-centimetre-to-litre equality.
Common mistakes
- Using a length factor for square or cubic units.
- Multiplying measurements written in incompatible units.
- Equating mass and capacity without density information.
What can you explain now?
How many litres are in 1 m³?
Compare with the explanation
1000 litres
1 m³ = 1 000 000 cm³, and each litre is 1000 cm³.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Tomorrow, convert one length, area and volume, explaining why the powers of the conversion factor differ.
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.
Original StudyForA teaching content · AI-assisted checks · Human teacher review pending.
Number contains 19 sequenced lessons; Algebra and graphs 21; Coordinate geometry 10; Geometry 15; Mensuration 13; Trigonometry 13; Transformations and vectors 11; Probability 7; Statistics 13. All 72 syllabus section entries now link to teaching and staged practice. Seven mixed checkpoints sample skills and suggest review lessons. Nine earlier overviews remain available. Full cumulative assessment and human teacher review remain pending. Written lesson practice, charts and constructions are self-checked, not automatically graded. Checkpoints do not save an exam grade or certify mastery.
Check the official syllabus 2025–2027 Open related practice and resources