Concept 4 of 4
Surface Area
Today's big idea
Surface area adds every outside face, which for a cuboid is 2(LW + LH + WH).
An open or cut solid is missing faces, so subtract those from the full skin.
How it works
👀 What's going on?
Volume asks how much fits inside a box. Wrapping paper asks something else, because paper only ever touches the outside. Surface area is the total area of every face.
💡 Here's the trick
Look at the net above. The box has been unfolded flat, and the six faces are now six ordinary rectangles you can measure. Add all six areas and you have the surface area.
🪄 How to do it
- 1.Find the three different faces on the net above.
- 2.Work out the area of each of those three.
- 3.Add them, then double for the matching pair.
✍️ Try it
What is the surface area of a cube of side 10 cm? Then: what is the surface area of a cuboid 9 cm by 5 cm by 2 cm?
The cube has 6 equal faces, so 6 × 100 = 600 cm². The cuboid gives 2 × (45 + 18 + 10) = 146 cm².
⚠️ Watch out
You might be thinking a cuboid has six different faces to work out. It really has only three, because every face has a twin on the opposite side. That is why you find three areas and then double the total.
🌟 Why this matters
Wrapping a present, painting a room and tiling the outside of a fish tank are all surface area jobs. None of them care how much fits inside, only how much skin the shape has.
Exam tip: An open box loses one face, so hunt for the words lid or open before you reach for a formula.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A cube has side 5 cm. What is the SURFACE AREA?”
- 1
A cube has 6 identical faces
Each face is a square. 📦
- 2
Area of one face
5 × 5 = 25 cm².
- 3
Total = 6 × face area
SA = 6 × 25
- 4
Answer ✓
SA = 150 cm².
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap each pair of faces to wrap it. Every pair counts twice — once for each side.
CUBE · ROUND 1 OF 3
4 × 4 × 4 cm
Wrapped so far: 0 cm²
Quick check
✅ VERIFICATION
A cuboid is 8 cm × 3 cm × 2 cm. What is its SURFACE AREA?
⚡ Finish the activity above first to answer.
Keep going!