Volume is how much space a solid takes up. We can measure it by counting unit cubes. In a solid cuboid some cubes are hidden at the back and in the middle, so don't count only the ones you can see. Count the cubes in the top layer (rows × cubes in each row), then multiply by the number of layers. Count cubes, not the square faces you can see: a corner cube shows three faces but is only one cube.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- volume
- the amount of space a solid takes up
- unit cube
- a cube used as one unit of volume
- layer
- one flat slice of cubes
Worked examples
A model is one layer of cubes, 4 cubes by 3 cubes. How many cubes?
- 1.One layer of 4 rows of 3.
- 2.4 × 3 = 12 cubes.
= 12
A solid cuboid is 3 cubes long, 2 cubes deep and 2 cubes high. How many cubes?
- 1.Top layer: 3 × 2 = 6.
- 2.2 layers: 6 × 2 = 12 cubes.
= 12
A solid cuboid is 4 cubes long, 3 cubes deep and 3 cubes high. How many cubes?
- 1.Top layer: 4 × 3 = 12, including hidden cubes.
- 2.3 layers: 12 × 3 = 36 cubes.
= 36
For parents
Method: Count a layer, times the layers
What to say: How many cubes are in one layer? How many layers are there?
Common mistakes:
- Counts only the cubes that can be seen and misses the hidden ones inside and at the back.
- Counts the visible square faces instead of the cubes.
- Counts only the cubes on the front face.
- Adds the number of cubes along each edge instead of multiplying.