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.