Learning Objectives
- explain volume as space inside a solid;
- calculate volumes of cubes and cuboids;
- find missing dimensions;
- convert between cubic units and capacity;
- solve packing and filling problems.
Introduction
This lesson develops Volume of Cubes and Cuboids from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Visual Exploration
Use the diagrams, tables or examples in this lesson to identify what changes, what stays fixed and which relationship connects the values.
Volume as Layers
Volume tells us how many unit cubes can fit inside a solid.
Formulas
Worked Example
Find the volume of a storage box 1.2 m by 80 cm by 50 cm.
Use one unit: 80 cm=0.8 m and 50 cm=0.5 m.
V=1.2×0.8×0.5=0.48 m³.
Volume and Capacity
Missing Dimensions
A cuboid has volume 360 cm³, length 10 cm and width 6 cm. Find height.
h = 360÷(10×6)=6 cm.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
Foundation- Find the volume of a cube with side 7 cm.
- Find the volume of a cuboid 12 cm by 5 cm by 4 cm.
- A cuboid has volume 480 cm³, length 12 cm and width 8 cm. Find height.
- A tank measures 1.5 m by 0.8 m by 0.6 m. Find its capacity in litres.
- How many cubes of side 2 cm fit exactly into a cuboid 10 cm by 8 cm by 6 cm?
- A cube has volume 729 cm³. Find its surface area.
✅ Check Your Work
Show practice answers
- 343 cm³.
- 240 cm³.
- 5 cm.
- 1.5×0.8×0.6=0.72 m³=720 L.
- Large volume=480 cm³; small cube volume=8 cm³; number=60.
- Side=9 cm; surface area=6×81=486 cm².
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Volume measures space inside a solid.
- Cube: s³; cuboid: lwh.
- Use consistent units before calculating.
- 1 m³ = 1000 L.