Area, volume and surface area
Calculating the surface area of cubes and cuboids
Surface area is how much wrapping paper you would need. Unfold the box flat, add up every face, and that is your answer.
What surface area is
The SURFACE AREA of a cube or cuboid is the TOTAL AREA of all its faces. Because you are adding up areas, the units are SQUARE units: mm², cm², m² — never cubed. That is the quickest way to tell surface area from volume: volume is cubed, surface area is squared.
A cube is easy
A cube has SIX identical square faces. For a cube of side 2 cm: Area of one face = 2 × 2 = 4 cm² Surface area = 6 × 4 = 24 cm² One face, times six. That is the whole method.
A cuboid has three pairs
Unfold a cuboid into its NET and you can see the faces come in three matching pairs. • two faces of length × width • two faces of length × height • two faces of width × height Work out one of each, then double each one before adding.
Working through a cuboid
A cuboid is 8 cm by 5 cm by 3 cm. Top face: 8 × 5 = 40 cm² Front face: 8 × 3 = 24 cm² Side face: 5 × 3 = 15 cm² Surface area = 2 × 40 + 2 × 24 + 2 × 15 = 80 + 48 + 30 = 158 cm² Forgetting to double is the classic mistake — always check you have six faces, not three.
Worked examples
A cube of side 2 cm
- One face: 2 × 2 = 4 cm².
- A cube has 6 faces.
- 6 × 4 = 24.
Answer: 24 cm²
A cuboid 8 cm by 5 cm by 3 cm
- Top: 8 × 5 = 40. Front: 8 × 3 = 24. Side: 5 × 3 = 15.
- Double each: 80, 48, 30.
- 80 + 48 + 30 = 158.
Answer: 158 cm²
A cube of side 5 cm
- One face: 5 × 5 = 25 cm².
- 6 × 25 = 150.
Answer: 150 cm²
How many faces does a cuboid have?
- Unfold the net and count.
- They come in three matching pairs.
Answer: 6 faces, in 3 pairs
A cuboid 4 cm by 3 cm by 2 cm
- 4 × 3 = 12, 4 × 2 = 8, 3 × 2 = 6.
- 2 × 12 + 2 × 8 + 2 × 6 = 24 + 16 + 12.
Answer: 52 cm²
Why is surface area in cm² and not cm³?
- You are adding up areas of flat faces.
- An area uses two dimensions.
Answer: Because you are totalling areas, not filling space
Where you see this in real life
- The amount of card in a cereal box is its surface area, which is why packaging designers work to shrink it.
- Paint coverage is quoted per square metre, so a room is costed from the surface area of its walls.
Key words
- Surface area
- the total area of all the faces of a solid
- Face
- one flat surface of a solid
- Net
- a solid unfolded flat
- Cuboid
- a box shape with six rectangular faces
- Pair
- two matching faces on opposite sides