Volume measures space in cubic units; capacity measures how much a container holds. 1 cm³ holds 1 mL, 1000 cm³ holds 1 L, and 1 m³ holds 1000 L. A cubic metre is 100 × 100 × 100 = 1 000 000 cm³, not 100.
A 1 L milk carton and a 10 cm cube hold exactly the same amount. A cubic metre of water is a tonne. Why do the units fit together so neatly?
Volume is the space a solid takes up, in cubic units (cm³, m³). Capacity is how much a container holds, in millilitres (mL), litres (L) or kilolitres (kL). They link exactly:
Volume
Capacity
1 cm³
1 mL
1000 cm³ (a 10 cm cube)
1 L
1 m³
1000 L = 1 kL
A cubic metre is 100 cm × 100 cm × 100 cm = 1 000 000 cm³: a length conversion is used three times, once for each direction.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
A 10 cm cube
How many cubic centimetres is it, and how many millilitres is that?
TryTry it on the board and compare the result with your prediction.
Fill a box
The panel gives the volume and the capacity together.
Try it yourselfYour edits are saved in this browser.
Make a box that holds exactly 1 L. Was your prediction right? Could a box with different lengths also hold 1 L?
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
Converting units
Read Ravi's working. How many cm are in each direction of a cubic metre?
How many litres does 1 m³ hold?
Ravi works out how much a 2 m³ tank holds. Click the line where his working goes wrong.
ModifyChange the problem on purpose and see what happens.
Tanks and cartons
Need a hint?
24 000 L is 24 m³.
Another hint
Try a base of 4 m by 3 m.
Try it yourselfYour edits are saved in this browser.
Make a water tank that holds 24 000 L.
Use the board. This ticks when you get there.
A jug holds 2.5 L. How many cm³ is that?
A cup holds 350 mL. How many cm³ is that?
PractiseA few on your own, to check you have it.
Volume and capacity
Write 4500 mL in litres.
A container holds 0.6 m³. How many litres is that?
A box is 20 cm by 15 cm by 10 cm. How many litres does it hold?
Review: a triangular prism has a right-triangle end with legs 3 cm and 4 cm, and is 10 cm long. What is its volume in cm³?
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
A juice carton
Then say which of your designs would fit best in a lunch box, and why.
Try it yourselfYour edits are saved in this browser.
Need a hint?
600 mL = 600 cm³.
Another hint
Try a base of 10 cm by 6 cm.
Design a carton that holds 600 mL, with a base that is not square (l more than w).
Use the board. This ticks when you get there.
For teachers
Students build boxes and tanks, read their volume and capacity together, and convert between cm³, mL, L and m³ (AC9M8M02, node 1). About 35 minutes.
Do the Run board yourself first. Bring a 1 L carton and a 10 cm cube (or a drawing) if you can.
The one idea: 1 cm³ holds 1 mL, so 1000 cm³ is 1 L, and 1 m³ (100 × 100 × 100 cm³) is 1000 L. The common mistake is converting a cubic unit with the length factor once (Ravi's mistake).
The board gives capacity in mL or L for cm and in L for m.
Wider: why a cubic metre of water has a mass of about a tonne, and water storage in kilolitres or megalitres (dams, town water).
Running the lesson
Predict: ask students to show the size of a litre with their hands.
Run: ask for two different boxes that hold 1 L.
Investigate: ask Ravi to draw his cubic metre.
Modify: ask which unit a council would use for a dam.
Make: ask whose carton is easiest to hold.
The hard part (on purpose)
Converting cubic units. Ask students to draw a cube and label 100 cm on all three edges before they convert.
When students get stuck
A student says 1 m³ = 100 cm³. Ask: How many cm along each of the three edges? Fix: 100 × 100 × 100 = 1 000 000 cm³.
A student mixes up cm and cm³. Ask: Is that a length, an area or a volume? Fix: Cubic units for volume.
A student divides by 100 for mL to L. Ask: How many mL in a litre? Fix: 1000 mL = 1 L.
Stretch and support
Stretch: A rainwater tank is 2 m long, 2 m wide and 1.5 m tall. How many days would it supply a family that uses 180 L a day?
Support: Keep the conversion table visible; use real containers labelled in mL and L.
Where it leads
This starts AC9M8M02.
Where it leads: prism problems (next lesson), and volume of cylinders (Year 9).
What each step is for
a 10 cm cube: Committing to how much a 10 cm cube holds shows whether they link cm³ to mL, and the size of a litre.
fill a box: Building boxes and reading their volume and capacity side by side shows cm³ and mL are the same number.
converting units: 1 m³ = 1000 L; converting cubic units uses the length factor three times (Ravi uses it once); the unit should suit the context.
tanks and cartons: Building a tank in metres, converting both ways, and the difference between cm and cm³.
volume and capacity: Conversions both ways and a box's capacity, mixed; using 100 instead of 1 000 000 for m³ is the planted slip; the triangular prism review keeps base times height fresh.
a juice carton: Designing to a capacity with a constraint uses volume and capacity together.