Volume of a rectangular prism

It counts cubes, in two stages

Cover the floor. A base $6$ by $4$ holds $24$ unit cubes — that is the rectangle’s area, earning its keep.

Then stack. A box $3$ cubes tall holds $3$ identical layers of $24$:

$$24 \times 3 = 72$$

Multiplication counts equal groups, and the layers are equal groups.

Why the units are cubed

Each unit cube is one centimetre in all three directions — one cubic centimetre, written cm³.

Multiplied	Quantity	Units
one	perimeter	cm
two	area	cm²
three	volume	cm³

The exponent counts the dimensions. If three lengths were multiplied the units carry a $3$, and if they do not, a factor was missed.

Bh is the general form

$$V = Bh$$

This is the same product grouped differently — $B$ is already $l \times w$ for a box. Its advantage is that it keeps working when the base is not a rectangle: a prism with a triangular base has volume $Bh$ with $B$ being the triangle’s area.

One formula, any prism.

A cube

$$V = s^3$$

Where “cubed” for a third power comes from: $s^3$ is the volume of a cube with edge $s$.

Rearranged

$$h = \frac{V}{lw} \qquad l = \frac{V}{wh}$$

Divide by the product of the two dimensions you know.

Volume is not surface area

	Measures	Units
volume	what fits inside	cm³
surface area	the wrapping outside	cm²

Different questions, different units. And stopping after two dimensions gives the base area, not the volume — the commonest slip here, and the units expose it. See volume of a rectangular prism.