Rectangular Prism Volume

Length times width times height is less a formula than the definition of volume made arithmetic. Lay unit cubes across the floor of the box, $l$ of them one way, $w$ the other, so $lw$ cubes in a single layer, then stack $h$ layers. Counting them is the volume, and $V = lwh$ is that count written down. Every other volume formula on this site is ultimately a way of getting back to this one, by slicing an awkward solid into pieces that behave like boxes.

A worked instance from a job site: a strip footing 2.0 m long, 500 mm wide and 300 mm deep takes $2.0 \times 0.5 \times 0.3 = 0.30$ m³ of concrete. Each dimension recovers by division, so a 0.30 m³ pour spread 100 mm deep over a 2.0 m length must be 1.5 m wide.

The conversion worth memorising lives here. One cubic metre is exactly 1000 litres, because a litre is a cube 100 mm on a side and a thousand of those fill a metre cube. So a rectangular tank 1.5 m by 0.8 m filled to 1.1 m holds $1.32$ m³, which is 1320 litres, and that litre figure is the one you need before dosing anything into it at so many millilitres per litre. In imperial the same step runs through 1 ft³ = 7.48 US gallons.

The mistakes here are all about units, and they are expensive. The first is mixing units between the three dimensions, which is almost guaranteed when a slab is quoted in metres but its thickness in millimetres. A pad 6 m by 4 m by 100 mm is 2.4 m³; entered as 6 × 4 × 100 it reads 2400, a thousandfold error that looks like a plausible number of something. Convert every dimension to one unit before multiplying, never afterwards. The second is the scale factor between cubic units: cm³ to m³ is a million, not a hundred, because the conversion is cubed along with the length. The third is applying this to something that is not a box. Real excavations batter outward, real rooms are out of square, and real tanks have dished ends; for those, split the shape into parts, or use an average dimension and accept that you now have an estimate rather than an answer.