Primary 6 maths · Measurement & time · About 12 minutes
Use square and cube roots to recover dimensions
Work out the known face first, then divide the volume by it.
Start the interactive lesson →Open practice activity
What you will learn
- Use square and cube roots to recover dimensions
Models used: number sentences, stories, diagrams.
Before you start
Recover the missing layers
The cuboid contains 36 cubes. Its base is 4 by 3, so each layer contains 12.
Count cubes across a layer, then count the layers. Some cubes are hidden.
The cuboid contains 36 cubes. Its base is 4 by 3, so each layer contains 12.
4 × 3 = 12 cubes per layer
A volume of 60 cm³ on a 5 cm by 4 cm base has height 60 ÷ 20 = 3 cm.
Width 4, height 1, depth 3
Count cubes across a layer, then count the layers. Some cubes are hidden.
Two layers contain 24 cubes. We need one more layer to reach 36.
Width 4, height 2, depth 3
Count cubes across a layer, then count the layers. Some cubes are hidden.
There are three layers, so the height is 3 units.
height = 36 ÷ 12 = 3
Width 4, height 3, depth 3
What did the picture help us see?
There are three layers, so the height is 3 units.
Worked example: A new example, together
A cube has volume 27 cm³. Find its edge length.
Work out the known face first, then divide the volume by it.
Roots undo repeated multiplication of the same edge length.
Every edge of a cube has the same length. Equal edges multiply three times to give volume.
Every edge of a cube has the same length. A cube has volume 27 cm³. Find its edge length.
3 cm
Equal edges multiply three times to give volume.
Every edge of a cube has the same length. Use the cube root of 27.
Every edge of a cube has the same length. 3 × 3 × 3 = 27.
Every edge of a cube has the same length. Check the result against the question we started with.
3 × 3 × 3 = 27.
We found 3 cm. Roots undo repeated multiplication of the same edge length.
Every edge of a cube has the same length.
Common mistakes to discuss
- Dividing by one edge only. Volume is the product of three lengths. With volume 60 cm³ on a 5 cm by 4 cm base, the height is 60 ÷ 20 = 3 cm.
Check your understanding
- Use square and cube roots to recover dimensions
- work back from a volume to a missing dimension
- 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.
Try this lesson →Related Primary 6 lessons
- Find unknown dimensions of a cube or cuboidFind unknown dimensions of a cube or cuboid · About 12 minutes
- Relate volume base area and heightRelate volume base area and height · About 12 minutes