Mathematics 7–10 · Years 7–8
Volume of a rectangular prism: packing centicubes and filling with water
Measurement and space
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The idea
The volume of a prism is the number of unit cubes in one layer times the number of layers, and 1 cubic centimetre holds 1 millilitre, so a box measured in centimetres predicts the water it holds.
What you need
- 400 centicubes (1 cm plastic cubes) per group
- A rigid, waterproof open-top plastic container with a flat base and straight sides, internal dimensions about 10 cm by 8 cm by 5 cm (each group measures its own; moulded containers rarely measure whole centimetres inside and often taper slightly)
- A hollow plastic litre cube (10 cm internal edge)
- 250 mL and 1 L measuring jugs
- Water, tray and cloth
- Ruler
How to do it
- Measure the internal length, width and height of the container to the nearest millimetre; if the sides taper, measure the length and width halfway up.
- Cover the base with one layer of centicubes and count them (10 × 8 = 80). Predict how many layers fit and how many cubes in total.
- Fill the container layer by layer, counting cubes in as they go; record the total (400 for a 10 by 8 by 5 cm container).
- Empty the container, then fill it with water from the measuring jug and record the volume poured in (mL).
- Repeat the water step with the litre cube and record the volume (1000 mL, 1 L).
- Fill the container with water again and, over the tray, tilt it slowly so that water pours over one long top edge, stopping when the water surface just reaches the opposite bottom edge. The water left is a triangular prism with half the container's volume (the surface is the diagonal plane of the box); pour it into the jug and compare with half the rectangular result.
What you should see
A container whose inside measures exactly 10 × 8 × 5 cm takes 80 cubes per layer and 5 layers, 400 cubes, and holds 400 mL of water within about ±10 mL from jug reading and meniscus error. When the inside is not a whole number of centimetres the cubes fill only the whole-centimetre part: a box measuring 10.3 × 8.2 × 5.3 cm inside packs 10 × 8 × 5 = 400 cubes, while l × w × h = 447.6 cm³ and it holds about 448 mL, 12 per cent more than the count. The litre cube holds 1000 mL, showing 1000 cm³ = 1 L. The triangular prism of water left after tilting holds half the container's water, 200 mL for the 10 × 8 × 5 cm box. The learner knows it worked when l × w × h from the measured inside dimensions and the water volume agree within 3 per cent, and the cube count equals the product of the whole numbers of cubes that fit along each edge.
What changes
- What you change
- number of layers
- What you measure
- number of cubes (and water volume)
- What you keep the same
- same container
- cubes packed without gaps
- jug read at eye level
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Volume is the number of cubes visible on the outside.
- Doubling every dimension doubles the volume.
- Millilitres and cubic centimetres measure different things.
Safety card
Hazards
- water spills make floors slippery
Controls
- work over a tray
- wipe spills at once
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K–10 Syllabus (2022), Stage 4 Volume; page read 2026-09-22MA4-VOL-C-01
- Australian Curriculum v9AC9M7M02AC9M8M02
Sources
The pages the author read to write this activity.