Volume and Capacity
Capacity is how much a container can hold, measured in millilitres, litres, kilolitres and megalitres. In NSW Year 7 maths (NESA outcome MA4‑VOL‑C‑01) you link it to volume through two key facts: \(1\text{ cm}^3\) holds 1 mL, and \(1\text{ m}^3\) holds 1000 L.
You will find the volume of a tank or box and change it to litres, convert between mL, L, kL and ML, find the depth of water in a part-filled tank, work out how long a tap takes to fill a bath, count how many 250 mL cups a drink dispenser fills, and estimate how much rain falls on a paddock in kilolitres. It is part of Year 7 Area and Volume.
Theory
The capacity of a container is the amount it can hold, measured in millilitres (mL), litres (L), kilolitres (kL) and megalitres (ML). Volume and capacity are linked: \(1~\text{cm}^3 = 1\) mL, \(1000~\text{cm}^3 = 1\) L and \(1~\text{m}^3 = 1000\) L \(= 1\) kL. This Year 7 maths page shows how to find a capacity from a volume.
A cube with \(1\) cm edges holds exactly \(1\) mL. A cube with \(10\) cm edges holds \(1\) L, and a cube with \(1\) m edges holds \(1000\) L: \(1~\text{cm}^3 = 1~\text{mL}\), \(1000~\text{cm}^3 = 1~\text{L}\), \(1~\text{m}^3 = 1000~\text{L} = 1~\text{kL}\).
Capacity units. \(1\) L \(= 1000\) mL, \(1\) kL \(= 1000\) L, \(1\) megalitre (ML) \(= 1000\) kL. To a smaller unit, multiply by \(1000\); to a bigger unit, divide by \(1000\).
Method. Find the volume first with \(V = l \times w \times h\), in cubic units. Then convert to mL, L or kL as a separate step. For a container that is not full, use the depth of the liquid as \(h\).
Choose a sensible unit. A teaspoon (\(5\) mL) or a drink: mL. A bucket, fish tank or petrol tank: L. A water tank or a pool: kL. A dam or a harbour: ML.
Water over land. Area in m\(^2\) \(\times\) depth in m gives m\(^3\), and \(1~\text{m}^3 = 1\) kL. Remember \(1\) ha \(= 10\,000~\text{m}^2\) and \(1000\) kL \(= 1\) ML.
The links:
How to find a capacity
- Find the volume, using the depth of the liquid if it is not full.
- Convert: cm\(^3\) to mL (same number) or L (\(\div\,1000\)); m\(^3\) to kL (same number) or L (\(\times\,1000\)).
- Answer in the unit asked for.
(i) \(3.2\) L to mL
(ii) \(4500\) L to kL
(iii) \(6800\) kL to ML
| \(3.2 \times 1000\) | \(=\) | \(3200\) |
| \(4500 \div 1000\) | \(=\) | \(4.5\) |
| \(6800 \div 1000\) | \(=\) | \(6.8\) |
(i) \(3200\) mL
(ii) \(4.5\) kL
(iii) \(6.8\) ML
| \(45 \times 20 \times 30\) | \(=\) | \(27\,000\) |
| \(27\,000 \div 1000\) | \(=\) | \(27\) |
\(27\) L
(i) How many litres of water are in it?
(ii) How many more litres will fill it?
| \(2.4 \times 0.5 \times 0.4\) | \(=\) | \(0.48\) |
| \(0.48 \times 1000\) | \(=\) | \(480\) |
| \(2.4 \times 0.5 \times 0.6\) | \(=\) | \(0.72\) |
| \(720 - 480\) | \(=\) | \(240\) |
(i) \(480\) L
(ii) \(240\) L more
(i) How many litres are poured in?
(ii) How deep is the water in the tank?
| \(40 \times 25 \times 18\) | \(=\) | \(18\,000\) |
| \(60 \times 50\) | \(=\) | \(3000\) |
| \(18\,000 \div 3000\) | \(=\) | \(6\) |
(i) \(18\) L
(ii) \(6\) cm deep
| \(0.5 \times 10\,000\) | \(=\) | \(5000\) |
| \(5000 \times 0.02\) | \(=\) | \(100\) |
\(100~\text{m}^3 = 100\) kL \(= 0.1\) ML
| \(1.8 \times 1000\) | \(=\) | \(1800\) |
| \(1800 \div 20\) | \(=\) | \(90\) |
| \(90 \div 60\) | \(=\) | \(1.5\) |
\(90\) minutes, or \(1.5\) hours
Common pitfalls
Frequently asked questions
What is the difference between volume and capacity?
Volume is the space a solid takes up; capacity is how much a container holds.
How many millilitres are in a cubic centimetre?
\(1\).
How many litres are in a cubic metre?
\(1000\), which is \(1\) kL.
How do you find the capacity of a box in litres?
Find the volume in cm\(^3\), then divide by \(1000\).
What is a megalitre?
\(1000\) kL, or one million litres.