GCSE MATHS • HIGHER TIER
Cubes and Cuboids Made Simple
Recognise cube and cuboid properties, calculate volume and surface area, use nets and find missing dimensions.
Clear method
Exam practice
Worked proofs
Cubes and Cuboids in Four Moves
1
Identify
Decide whether the 3D shape is a cube or a cuboid.
2
Choose
Decide whether the question asks for volume, surface area or a missing dimension.
3
Calculate
Select the correct formula and substitute the measurements carefully.
4
Check
Calculate accurately and include the correct square or cubic units.
What You’ll Learn
Recognise the properties of cubes and cuboids.
Calculate the volume of cubes and cuboids.
Calculate surface area.
Find missing side lengths and dimensions.
Understand nets of cubes and cuboids.
Use correct square and cubic units.
Key Rules
Volume of a Cube
Volume = side³
Volume of a Cuboid
Volume = length × width × height
Surface Area of a Cube
Surface Area = 6 × side²
Surface Area of a Cuboid
Surface Area = 2(lw + lh + wh)
Worked Proof: Cubes and Cuboids
How to Solve Cube and Cuboid Questions
- 1. Identify whether the shape is a cube or cuboid.
- 2. Decide whether the question asks for volume, surface area or a missing dimension.
- 3. Choose the correct formula.
- 4. Substitute values carefully.
- 5. Calculate accurately.
- 6. Include correct units.
More Worked Examples
1
Question: A cube has side length 7 cm.
Volume = 7³
= 343 cm³
= 343 cm³
Volume of a Cube
2
Volume of a Cuboid
Question: A cuboid has dimensions 8 cm, 5 cm and 3 cm.
Volume = 8 × 5 × 3
= 120 cm³
= 120 cm³
3
Surface Area of a Cube
Question: A cube has side length 5 cm.
Surface Area = 6 × 5²
= 6 × 25
= 150 cm²
= 6 × 25
= 150 cm²
4
Surface Area of a Cuboid
Question: A cuboid measures 8 cm × 4 cm × 3 cm.
Surface Area = 2(32 + 24 + 12)
= 2(68)
= 136 cm²
= 2(68)
= 136 cm²
- Common GCSE Mistakes
- Confusing surface area and volume.
- Forgetting cubic units for volume.
- Using the wrong formula.
- Making arithmetic errors.
- Forgetting that cubes have equal edges.
- Exam Tips
- Identify the 3D shape before choosing a formula.
- Use cm² or other square units for surface area.
- Use cm³ or other cubic units for volume.
- Check that all three cube edges are equal.
- Write the formula before substituting values.
- For missing dimensions, rearrange the volume relationship carefully.
Skills Used in Cubes and Cuboids
3D Shape Properties
Volume
Surface Area
Nets
Mensuration
Missing Dimensions
Square Units
Cubic Units
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch theCubes and Cuboids Tutorial
Step-by-step walkthroughs of Cubes and Cuboids with clear methods and exam tips.
Frequently Asked Questions
A cube has six identical square faces.
A cuboid has rectangular faces and its length, width and height do not have to be equal.
Volume = side³.
Volume = length × width × height.
Surface area uses square units such as cm².
Volume uses cubic units such as cm³.