🧱 See It
Picture an empty box. Now fill the bottom of it with small cubes, all the same size, packed in neat rows with no gaps — that's one layer. To fill the whole box, you'd keep stacking identical layers on top of each other until you reach the top.
Volume is just how many unit cubes it takes to completely fill a space — count the cubes in one layer, then count how many layers it takes.
A box that's 4 cubes long, 3 cubes wide, and 5 layers tall is filled with 4 × 3 × 5 cubes in total.
✏️ Draw It
Here's that box drawn as an actual 3D box, with its three dimensions labelled. The grid on top shows the 4-across, 3-deep layer you're about to look at more closely:
A real 3D box, not just a flat rectangle — the top face shows exactly where that 4-by-3 layer of cubes sits.
Now look at just one base layer of unit cubes — 4 across and 3 deep:
This layer has 4 × 3 = 12 cubes. This exact layer repeats for every unit of height — stack it 5 times to fill the box.
🔢 Write It
Instead of stacking layer by layer, multiply all three dimensions at once:
Volume = length × width × height
Volume tells you how much space a solid takes up, measured in cubic units (like cm³). Capacity is the same idea, but for how much a container can hold — usually measured in liquid units like millilitres (mL) or litres (L).
💡 Worked Examples
Example — A box measuring 4 cm × 3 cm × 5 cm:
- Write the formula:
Volume = length × width × height - Substitute the numbers:
Volume = 4 × 3 × 5 - Multiply step by step:
4 × 3 = 12, then12 × 5 = 60 - Answer:
Volume = 60 cm³
Now convert to capacity:
- Remember:
1 cm³ = 1 mL - So
60 cm³holds exactly60 mL - Answer: this box can hold 60 mL of liquid.
🧠 Quick Reference
Area only needs two dimensions (a FLAT surface).
Always ask: is this shape flat (2D) or solid (3D)? — that tells you which formula to use.