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Volume of a prism, layer by layer

Years 5–8Stage 3 to Stage 4Move it

Build a prism from centimetre cubes, one layer at a time. Count the cubes in a layer, and the layers.

Demonstration: a simplified modelNot to scale1 · One layer

A rectangular prism made of centimetre cubes, 4 cm long, 3 cm wide and 3 cm high, drawn from the front, the right and above. One layer covers the base: 3 rows of 4 cubes, 12 cubes. Layers stacked: 1 of 3, so 12 cubes so far.

Each cube is 1 cm³. 3 equal rows of 4 cubes make one layer: 12 cubes.

  1. One row: 4 cubes
  2. One layer
  3. One cube: 1 cm³

Key Dashed outline: a layer still to stack. A dot: a cube hidden inside when the layers are stacked. Teal: half a cube, cut by the sloping side. Short dashes: the square that the triangle is half of.

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The idea, step by step

Not to scale

  1. A rectangular prism made of centimetre cubes, 4 cm long, 3 cm wide and 3 cm high, drawn from the front, the right and above. One layer covers the base: 3 rows of 4 cubes, 12 cubes. Layers stacked: 3 of 3, so 36 cubes so far.
    2 · Stack the layers3 equal layers of 12 cubes: 12 × 3 = 36 cubes. The box's volume is 36 cm³.1 One row: 4 cubes · 2 One layer · 3 One cube: 1 cm³
  2. A rectangular prism of centimetre cubes, 4 cm long and 3 cm wide, with its 3 stacked layers lifted apart so the top of every layer shows: 12 cubes in each, 36 in all. A dot marks each of the 12 cubes the stack hid from the front, the right and above.
    3 · Look insideStacked, only 24 cubes show from outside. Lifted apart, the dots mark 12 more that were hidden inside.
  3. A rectangular prism made of centimetre cubes, 6 cm long, 3 cm wide and 2 cm high, drawn from the front, the right and above. One layer covers the base: 3 rows of 6 cubes, 18 cubes. Layers stacked: 2 of 2, so 36 cubes so far.
    4 · A bigger base, fewer layersA bigger base but fewer layers: 18 × 2 = 36 cubes, the same as the box.1 One row: 6 cubes · 2 One layer · 3 One cube: 1 cm³
  4. A prism made of centimetre cubes on an L-shaped base of 5 squares, 4 cm high, drawn from the front, the right and above. One layer covers the base: 5 cubes. Layers stacked: 4 of 4, so 20 cubes so far.
    5 · An L-shaped baseRows of 3 and 2 make an L-shaped layer of 5 cubes. 4 layers: 5 × 4 = 20 cubes.1 One row: 2 cubes · 2 One cube: 1 cm³ · 3 One layer
  5. A prism made of centimetre cubes on a right-angled triangle base whose two short sides are both 4 cm, 3 cm high, drawn from the front, the right and above. The sloping side cuts cubes in half, so one layer holds 6 whole cubes and 4 half cubes: 8 cubes. Layers stacked: 3 of 3, so 24 cubes so far.
    6 · A triangular baseThe sloping side cuts cubes in half: 6 whole and 4 halves make 8 cubes a layer. 3 layers: 24 cubes.1 One cube: 1 cm³ · 2 Half a cube

Each stacked layer, and the volume so far

LayerWhole cubes in itHalf cubes in itVolume so far (cm³)In the first figure
112012.0Shown

Try it in the Lab

Practicals with real materials, each with its safety card.

Learn it in a lesson

With a learner

Three questions to ask

  1. How many cubes are in one layer of the box, and how can you tell without counting them one by one?
  2. How many cubes are hidden inside the box, where you cannot see them from any side?
  3. How can you tell, before building it, whether a base six by three, two layers high, holds more cubes than the box?

What to expect

Many learners count only the cubes they can see, or add the three lengths. Stacking the layers one at a time, then lifting them apart, shows every cube.

What to try next

Pack a box with centimetre cubes, layer by layer, in Try it in the Lab, above. Then work out an L-shaped or triangular prism with the right prisms lesson in Learn it in a lesson.

About this model

What is simplified

  • The prism is drawn the way textbooks draw a stack of cubes: the front face true shape, and depth sloping up to the right at half its length. So the drawing is not to scale, and a length on the screen is not a length in centimetres.
  • The drawing is fitted to the stage, so a cube is drawn smaller in a bigger prism, and smaller again when the layers are lifted apart.
  • The cubes fit together exactly, with no gaps and square edges, so they fill the prism with nothing left over. Real centimetre cubes are close to this.
  • A triangle base here always has its two short sides equal, so its sloping side cuts every cube it crosses exactly in half. A triangle with unequal sides cuts cubes into other pieces, and its volume is still base area × height.
  • A layer is lowered onto the stack at a steady pace so you can watch the stack grow. No time is shown, and none is taught.
  • The model counts every cube and half cube in every layer. It never uses a formula, so the layers-times-cubes rule is a result, not an assumption.
  • A cylinder's round base cannot be covered exactly by centimetre cubes, but it has the same slice all the way up, so its volume is also base area × height. The cylinder lesson in Learn it in a lesson, above, works it out.

Review

Demonstration: a simplified model. Checked against its written sources, 26 September 2026. Not reviewed by a qualified teacher.

Curriculum references

MA3-3DS-02MA4-VOL-C-01AC9M7M02AC9M8M02

Reference, not a verified alignment.

All demonstrations Practicals in the Lab