Key stage 2 maths, ages 9 to 11, about 15 minutes
Volume of Cubes and Cuboids
Count the cubes that fill a box, then find its volume without counting them all.
Box of cubes: fill it with cubes
A cuboid 4 cm long, 3 cm wide and 2 cm high, built from cubes of 1 cm³. One layer holds 4 × 3 = 12 cubes. 2 of 2 layers are filled, which is 24 cubes. The volume is 4 × 3 × 2 = 24 cm³. Each cubic centimetre holds 1 ml, so the box holds 24 ml.
Ten questions, each in steps. A question counts only if every step is right first time. New numbers every time.
Why this mission needs it: Propellant tanks, cargo bays and pressurised crew modules are three-dimensional spaces: volume tells you how much fuel or air they can hold.
The idea
- Volume, cubic units, such as cm³ or m³
- The space the solid takes up, counted in cubes.
- Length, a length, such as cm or m
- How long the box is, from one end to the other.
- Width, a length, such as cm or m
- How wide the box is, across its base.
- Height, a length, such as cm or m
- How tall the box is, from its base to its top.
Counting cubes
A cube with edges 1 cm long has a volume of 1 cubic centimetre, written 1 cm³. To find how much space a box takes up, imagine filling it with these cubes and counting them.
Key point: Volume is measured in cubic units: cm³ for small things, m³ for big things such as rooms and pools.
Layer by layer
Cover the base of a box 4 cm long and 3 cm wide with cubes: one layer holds cubes. If the box is 2 cm high, two layers fit, so it holds cubes. Its volume is 24 cm³.
Key point: One layer is length × width cubes, and the height says how many layers there are. So .
Cubes
In a cube, every edge is the same length. A cube with edges of 3 cm holds small cubes, so its volume is 27 cm³.
Key point: For a cube, multiply the edge by itself, then by itself again.
Volume and capacity
A container's capacity is the amount it can hold. Every cubic centimetre of space inside it holds 1 millilitre, so a tank with a volume of 1,000 cm³ holds 1 litre.
Key point: 1 cm³ is 1 ml, and 1,000 cm³ is 1 litre.
Working back
If you know the volume and two of the edges, you can find the third. A box with a volume of 30 cm³ and a base 5 cm by 2 cm has 10 cubes in each layer, so it must be cm high.
Key point: Divide the volume by one layer (length × width) to find the height.
Where you’ll see this: Builders order concrete by the cubic metre, and the space inside a fridge, a fish tank or a car boot is usually given in litres, which is a measure of volume too.
Worked example
A storage module on a moon base is a cuboid 5 m long, 4 m wide and 3 m high. What is its volume?
- 1Imagine filling it with cubes 1 m along each edge. One layer on the floor holds cubes.
- 2The module is 3 m high, so 3 layers fit: cubes.
- 3Each cube is 1 m³, so the volume is 60 m³. The edges are in metres, so the volume is in cubic metres.
- 4Check with the rule: .
Answer
Practice
Practise with the step-by-step quiz in the Try it panel. Each question is answered one step at a time, with fresh numbers every time, and the questions you miss come back for review.
Notes
Volume of cubes and cuboids
In the last lesson, area counted the squares that cover a flat shape. Volume counts the cubes that fill a solid shape.
What volume is
The volume of a solid is how much space it takes up. It is measured by counting cubes of a standard size:
- 1 cubic centimetre (1 cm³) is a cube with edges 1 cm long.
- 1 cubic metre (1 m³) is a cube with edges 1 m long, big enough for a child to sit inside.
Very small volumes can be measured in cubic millimetres (mm³), and very large ones, such as the water in a lake, in cubic kilometres (km³).
Cuboids
A cuboid is a box shape: every face is a rectangle, and every angle is a right angle. It is measured by its length, its width and its height.
Filling a cuboid layer by layer
Take a box 6 cm long, 2 cm wide and 4 cm high, and fill it with 1 cm cubes.
- The bottom layer has 2 rows of 6 cubes: cubes.
- The box is 4 cm high, so it takes 4 layers: cubes.
So the volume is 48 cm³.
The rule
Counting layers always works the same way, so there is a rule:
You can multiply the three edges in any order: and both make 48.
Cubes
A cube is a cuboid whose length, width and height are all the same. A cube with edges of 4 cm has a volume of cm³.
Units
The unit of the volume comes from the unit of the edges. Edges in centimetres give cm³, and edges in metres give m³. If the edges are in different units, change them to the same unit first.
Take care: 1 m³ is not 100 cm³ but cm³, because a 1 m cube is 100 small cubes long, 100 wide and 100 high.
Volume and capacity
Capacity is how much a container holds. A space of 1 cm³ holds exactly 1 millilitre (ml), so 1,000 cm³ holds 1 litre.
A fish tank 20 cm long, 10 cm wide and 10 cm high has a volume of cm³, so it holds 2 litres of water.
Finding a missing edge
A box has a volume of 72 cm³ and a base 6 cm by 3 cm. One layer holds cubes, so the number of layers is . The box is 4 cm high.
Working back in other ways
- A cube's edge. A cube-shaped tank holds 1,000 cm³. Which number, used three times in a multiplication, makes 1,000? , so each edge is 10 cm. That tank holds exactly 1 litre.
- How deep the water is. A fish tank has a base 30 cm by 20 cm. Pour in 12 litres, which is 12,000 cm³. A layer of water 1 cm deep is cm³, so the water is cm deep.
- How many bigger cubes fit. How many 2 cm cubes fit in a box 8 cm by 6 cm by 4 cm? Count along each edge: along the length, across and up, so cubes fit. Dividing the volume by 2 does not work, because each 2 cm cube is cm³, not 2 cm³.
Two cuboids together
To find the volume of two cuboids together, find each volume, then add. A moon base has a living module 6 m by 5 m by 3 m and a store 4 m by 2 m by 2 m:
- Living module: m³.
- Store: m³.
- Together: m³.
Comparing volumes
Box A is 8 cm by 2 cm by 2 cm, and box B is 4 cm by 3 cm by 3 cm. Box A is longer, but box B holds more:
| Box | Volume |
|---|---|
| A | cm³ |
| B | cm³ |
Estimating
To estimate a volume, round each edge first. A box 9.8 cm by 5.1 cm by 2 cm has a volume of about cm³.
Two common mistakes
- Adding the edges. For the 6 cm by 2 cm by 4 cm box, is not the volume. Volume counts cubes, so multiply.
- Stopping at one layer. is the area of the base, in cm². Multiply by the height to count every layer.
Next on the journey
A cube with edges of 5 cm holds small cubes. Using the same number three times in a multiplication, as in , is called cubing it. If you know a cube's volume, how do you find its edge? The next lesson is about powers and roots.
Sources
The topics in these notes follow the Department for Education document below. The litre is defined as 1,000 cm³ in the International System of Units.
- National curriculum in England: mathematics programmes of study (Department for Education)
- The International System of Units (SI brochure) (International Bureau of Weights and Measures)
Where this fits in the curriculum
Key stage 2, Years 5 and 6 in the curriculum for England.
The Department for Education says pupils should be taught to:
Year 5
“estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]”
Year 6
“recognise when it is possible to use formulae for area and volume of shapes”
Year 6
“calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³]”
Quoted from National curriculum in England: mathematics programmes of study (Department for Education, gov.uk), checked on 12 October 2026. This is the content every exam board has to cover. It is not one board’s specification, so use your own for exactly what is examined.
Tick it off once the practice questions make sense.
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