Primary 5 maths · Measurement & time · About 12 minutes
Find volumes of cubes and cuboids
Separate base dimensions, layer size and number of layers. Check what is known and what is missing.
Start the interactive lesson →Practise: Cube builders
What you will learn
- Find volumes of cubes and cuboids
Models used: number sentences, stories, diagrams.
Before you start
Count a layer, then stack the layers
One layer is 4 cubes wide and 3 cubes deep. It contains 12 cubes.
Count cubes across a layer, then count the layers. Some cubes are hidden.
One layer is 4 cubes wide and 3 cubes deep. It contains 12 cubes.
Width 4, height 1, depth 3
Count cubes across a layer, then count the layers. Some cubes are hidden.
Stack a second matching layer. Now there are two lots of 12 cubes.
Width 4, height 2, depth 3
Count cubes across a layer, then count the layers. Some cubes are hidden.
A third layer gives 36 cubes. Remember the cubes hidden inside.
12 + 12 + 12 = 36
Width 4, height 3, depth 3
What did the picture help us see?
A third layer gives 36 cubes. Remember the cubes hidden inside.
Worked example: A new example, together
Find the volume of a cuboid 2 cm by 5 cm by 2 cm.
Separate base dimensions, layer size and number of layers. Check what is known and what is missing.
Equal layers connect base area and height with total volume.
Each dimension is in centimetres. Count the cubes in one layer, then the equal layers. One layer contains 2 × 5 = 10 unit cubes.
Each dimension is in centimetres. Count the cubes in one layer, then the equal layers. Find the volume of a cuboid 2 cm by 5 cm by 2 cm.
20 cm³
There are 2 equal layers.
Each dimension is in centimetres. Count the cubes in one layer, then the equal layers. Count all layers: 10 × 2 = 20.
Each dimension is in centimetres. Count the cubes in one layer, then the equal layers. Check the result against the question we started with.
10 × 2 = 20.
We found 20 cm³. Equal layers connect base area and height with total volume.
Each dimension is in centimetres. Count the cubes in one layer, then the equal layers.
Common mistakes to discuss
- Adding the three edges. Volume multiplies length, breadth and height. A 2 cm by 5 cm by 3 cm cuboid holds 30 cm³, not 10 cm³.
Check your understanding
- Find volumes of cubes and cuboids
- explain volume or a missing dimension through equal layers
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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