How Much Does a Box Actually Hold?

Step 1 of 5

Volume asks how much space is inside.

Not the surface and not the edges, but the amount of room available for water, air or anything else you might pour into it.

Step 2 of 5

Start by tiling the bottom layer.

Lay unit cubes across the base until it is covered. That first layer is just an area problem, and it holds length times width cubes.

Step 3 of 5

Then stack identical layers to the top.

Every layer above the first holds exactly the same number of cubes, so the height simply tells you how many copies of that layer to add.

Step 4 of 5

That is why three measurements are multiplied.

Length times width gives one layer, and multiplying by height counts the layers. The familiar formula is really counting cubes.

Step 5 of 5

Small changes in size cause large changes in volume.

Doubling all three measurements makes eight times the volume, because each of the three directions doubles the count independently.

A cube 10 cm on each side holds exactly one litre, which is how the litre was originally defined.