Volume & cuboids

Will the aquarium fit on the dresser, and how much water does it need? Is one moving box enough for your books or do you need three? Questions like these are about volume: the space something takes up. Here you'll learn how to calculate it.

From area into space

You measure an area by covering it with little squares: a rectangle of 4 by 3 squares has an area of 12. For volume you do the same with little cubes. A cuboid is like a stack of such rectangle layers: the bottom layer has a · b cubes, and you stack c of these layers on top of each other.

The cuboid formula

That gives us the formula right away: V = a · b · c, that is length times width times height. Put differently: base area times height. A box 4 cm long, 3 cm wide and 5 cm high has a volume of 4 · 3 · 5 = 60 cubic centimetres, written 60 cm³. One cubic centimetre is the volume of a cube with 1 cm edges, roughly the size of a sugar cube. The formula also runs backwards: if you know the volume and the base area, you get the height by dividing the volume by the base area.

Litres, cm³ and dm³

For liquids you usually use litres. Luckily the conversion is simple: 1 litre is exactly 1 dm³, a cube with 10 cm edges. And because 10 · 10 · 10 = 1000, we get 1 l = 1000 cm³. An aquarium 40 cm long, 25 cm wide and 30 cm high holds 40 · 25 · 30 = 30000 cm³, which is 30 litres.