Concept 3 of 4
Volume
Today's big idea
Volume counts the cubes packed inside a solid, so a cuboid gives V = L × W × H.
Count the cubes layer by layer: the base is one layer, the height stacks the rest.
How it works
👀 What's going on?
Area filled a flat shape with squares. A box is not flat, so squares cannot do the job on their own. Volume fills the inside of a solid with little cubes instead.
💡 Here's the trick
Look at the box above. One layer across its base holds 10 × 6 = 60 cubes, and the box stacks 4 such layers. That is exactly why volume = length × width × height.
🪄 How to do it
- 1.Name the three edge lengths of the box above.
- 2.Multiply the first two to get one layer.
- 3.Multiply by the height to fill the solid.
✍️ Try it
What is the volume of a cuboid 6 cm by 4 cm by 3 cm? Then: how many litres fill a tank 25 cm by 20 cm by 16 cm?
The cuboid gives 6 × 4 × 3 = 72 cm³. The tank holds 8,000 cm³, and 1,000 cm³ makes 1 litre, so that is 8 L.
⚠️ Watch out
You might be thinking a litre is 100 cm³, since 100 turns up in so many conversions. Cubes stack in three directions, so the jump is 10 × 10 × 10. One litre is 1,000 cm³, a box of side 10 cm.
🌟 Why this matters
Water tanks, cartons and fridges are all sized by volume, which is how you know whether a suitcase will swallow your gear. A litre of milk is exactly a 10 cm cube of space.
Exam tip: Convert everything to one unit before you multiply, since a paper loves mixing metres with centimetres.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A cuboid is 10 × 6 × 4 cm. What is its VOLUME?”
- 1
Recall the formula
V = L × W × H. 🧊
- 2
Substitute
V = 10 × 6 × 4
- 3
Multiply two at a time
10 × 6 = 60. 60 × 4 = 240.
- 4
Re-state with units ✓
Volume = 240 cm³.
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap to stack layers. Each layer is one base (length × width) of cubes.
CUBOID · ROUND 1 OF 3
base 3 × 2 = 6 cubes · height 4
Layers stacked: 0 of 4 · Volume = 6 × 0 = 0 cm³
Quick check
✅ VERIFICATION
A cuboid is 7 cm × 5 cm × 4 cm. What is its VOLUME?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Surface Area
6 × side² · 2(lw + lh + wh).