Volume units go up and down by the cube of the length factor, and capacity links to volume through one fact: 1 litre = 1000 cm³. Get those two ideas clear and most unit marks become safe.
This lesson follows work with a cylinder and a cone, because answers there often need turning into litres. It belongs to volume and capacity.
What are the key facts?
| Fact | Why |
|---|---|
| 1 cm³ = 1 millilitre (mL) | Definition used in measurement |
| 1 litre = 1000 mL = 1000 cm³ | A 10 cm cube |
| 1 m³ = 1000 litres | 1 000 000 cm³ ÷ 1000 |
| 1 m³ = 1 000 000 cm³ | 100 × 100 × 100 |
| 1 cm³ = 1000 mm³ | 10 × 10 × 10 |
How to convert
- Write the length factor, for example 1 m = 100 cm.
- Cube it. 100³ = 1 000 000.
- Multiply to go to the smaller unit (m³ to cm³), or divide to go to the larger unit.
- For capacity, change to cm³ first, then divide by 1000 for litres.
Worked example
A rectangular tank is 80 cm long, 50 cm wide and 40 cm high. How many litres of water does it hold when full?
Step 1, volume: 80 × 50 × 40 = 4000 × 40 = 160 000 cm³.
Step 2, to litres: 160 000 ÷ 1000 = 160 litres.
Now convert the same volume to m³. Since 1 m³ = 1 000 000 cm³, 160 000 ÷ 1 000 000 = 0.16 m³. Check: 0.16 m³ × 1000 = 160 litres, which agrees.
The mistake to watch for
The usual slip is to convert the volume with the length factor, once only.
Mistaken working: 2.4 m³ = 2.4 × 100 = 240 cm³
This treats the volume as a length.
The correction is to cube the factor: 2.4 × 1 000 000 = 2 400 000 cm³. A quick sense check helps: a cm³ is tiny, about the size of a sugar cube, so a cubic metre must contain a very large number of them.
Check yourself
1. Write 3.5 litres in cm³.
Show answer
3.5 × 1000 = 3500 cm³.
2. A skip has volume 0.75 m³. How many litres is that?
Show answer
1 m³ = 1000 litres, so 0.75 × 1000 = 750 litres.
3. A cuboid container measures 25 cm by 20 cm by 12 cm. How many litres can it hold?
Show answer
Volume = 25 × 20 × 12 = 500 × 12 = 6000 cm³. Then 6000 ÷ 1000 = 6 litres.
4. Convert 4500 mm³ to cm³.
Show answer
1 cm³ = 1000 mm³, so 4500 ÷ 1000 = 4.5 cm³.
Where this leads next
With units under control, move on to solving a reverse-dimension volume problem, where you start from a capacity and must work back to a length. The percentage-base explorer is a different tool, but the same habit of writing the base before the calculation applies.
Unit errors are easy to make and hard to spot in your own work. In online one-to-one Mathematics tuition, a teacher can watch your working and point out exactly where a factor went missing.