Topics · Primary Maths · Volume of Solids
Volume: counting cubes, and the litres that fill them
Volume is how much space something takes up, or how much a container holds. Counted in cubes for a solid and in millilitres for a liquid — and those two units are the same size, which is what most questions are really about.
- 226 exam papers analysed
- appears in 78% of P6 Maths papers
- ~4 min read
01 One cube is the unit
A cube measuring 1 cm each way is one cubic centimetre, written 1 cm³. Volume is how many of those fit inside a shape — nothing more complicated than that.
The little 3 is the whole point, in the same way the 2 in cm² was. Length uses cm, area uses cm², volume uses cm³, and giving an answer in the wrong one is answering a different question.
02 Where the formula comes from
Count the cuboid above and there are 24. You never have to count them one at a time, because they come in neat layers.
The bottom layer is 4 × 2 = 8 cubes. There are 3 such layers stacked up, so 8 × 3 = 24. Written in one go that is length × width × height, and the formula is just the counting done quickly.
That is worth holding on to, because it tells you what to do when the solid is not a plain box. Cut it into boxes, work out each, and add — exactly as with composite figures in area.
03 Cubes and millilitres are the same size
1 cm³ holds exactly 1 ml. They are not roughly equal or a conversion to look up — a container with a volume of 1 cm³ holds 1 ml of water, because that is how the millilitre was defined.
So a tank measuring 10 cm by 10 cm by 10 cm has a volume of 1000 cm³, and holds 1000 ml, which is 1 litre. Those three numbers describe the same box.
Once that clicks, a whole class of question stops being about conversion at all. Find the volume in cm³ and you already have the millilitres.
04 Tanks that are not full
Most P5 and P6 questions are about a rectangular tank holding some water. The move is nearly always the same: the water is itself a cuboid, and it has the tank's length and width but its own height.
- Volume of water = tank length × tank width × water height. Not the tank's height — the water's.
- Height of water = volume of water ÷ (length × width). The same relationship, rearranged.
- How much more will fit = full volume − water already in it.
- When something is dropped in, the water rises by exactly the volume of the object. A stone of 200 cm³ raises the level by 200 ÷ (length × width).
05 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- volumesayVOL-yoommore than onevolumes
How much space a solid takes up, or how much a container can hold. Measured in cm³ and m³, or in ml and litres for liquid.
- cubic centimetre, written cm³sayKYOO-bik SEN-ti-mee-tuhmore than onecubic centimetres
A cube measuring one centimetre each way. Volume is how many of these fit inside a shape. One of them holds exactly 1 ml.
- cuboidsayKYOO-boydmore than onecuboids
A box shape: six rectangular faces, every corner a right angle. Its volume is length × width × height.
- cubesaykyoobmore than onecubes
A cuboid whose edges are all the same length, so all six faces are squares. The way a square is a special rectangle.
- capacitysaykuh-PASS-uh-tee
How much a container holds, usually given in ml or litres. Volume is the space; capacity is what fits in it.
- litre, written lsayLEE-tuhmore than onelitres
1000 millilitres, and so 1000 cm³. A cube 10 cm each way holds exactly one litre.
06 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P2
Comparing which container holds more, and building solids from unit cubes.
Practise P2 Volume of Solids — 10 questions →38% of P2 papers
- P3
Counting unit cubes to find a volume, and measuring liquid in ml and litres.
Practise P3 Volume of Solids — 10 questions →20% of P3 papers
- P5
Volume of a cuboid by formula, and rectangular tanks part-filled with water.
Practise P5 Volume of Solids — 10 questions →54% of P5 papers
- P6
Finding a missing edge from a given volume, solids made of more than one cuboid, and objects dropped into water.
Practise P6 Volume of Solids — 10 questions →78% of P6 papers
07 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“The volume is 24 cm².”
cm² is area. Volume is measured in cubic units, cm³. The unit says which of the three questions you answered.
“To find the volume of water I multiply the tank's three measurements.”
That gives the volume of the whole tank. Water only reaches its own height, so use the water's height, not the tank's.
“1 cm³ is about 1 ml.”
It is exactly 1 ml, not approximately. Find a volume in cm³ and you have the millilitres already.
“A cube and a cuboid are different shapes.”
A cube is a cuboid whose edges happen to be equal — the same way a square is a rectangle. Every cube is a cuboid.
“The tank is 1 m each way, so the volume is 100 cm³.”
Convert before multiplying. 1 m is 100 cm, so it is 100 × 100 × 100 = 1,000,000 cm³. Mixing metres and centimetres inside one calculation is the commonest wrong answer on this topic.
Now try it
40 questions across 4 levels, marked as you go with the working shown.