lesson
Count cubes in layers
1 · Learn
Volume measures occupied three-dimensional space. In a cuboid, length × width counts unit squares in a base layer; multiplying by height counts the layers of unit cubes. Use consistent length units before multiplying.
Capacity describes how much a container can hold and is related to volume, but an object's outside dimensions may not give its usable internal capacity because walls take up space.
For larger spaces use cubic metres. A box 2 m long, 3 m wide and 4 m high has volume 24 cubic metres, not 24 square metres. A 1 m cube has edges of 100 cm, so it contains 100 times 100 times 100 = 1,000,000 cubic centimetres. Cubic-unit conversion changes three dimensions.
2 · Worked example
A cuboid 6 cm by 4 cm by 3 cm contains 6 × 4 × 3 = 72 cubic centimetres of space. A model can show three layers of 24 cubes.
3 · Your turn
Find the volume of a cuboid 8 cm by 5 cm by 2 cm. Is its area also 80 cm²?
Check your answer
The volume is 80 cm³. No: volume and surface area are different quantities; multiplying three lengths does not calculate area.
4 · Apply your learning
Build two different cuboids with the same number of unit cubes and compare their dimensions.
Adult guidance and safety
Ask the learner to explain the method and check it using a different representation. Supply place-value grids, fraction strips, accurate diagrams and measuring tools where needed. These examples need varied practice; a short correct answer alone does not establish fluency.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
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