Consider a right polyhedron with the length of [[$ 4 $]] cm, width of [[$ 2 $]] cm and height of [[$ 3 $]] cm.

The volume of a right polyhedron is determined by examining how many times a selected unit of measurement fits inside the polyhedron. Since the dimensions of a rectangle are given in centimeters, it is natural to choose a cube that is one centimeter long on all sides as the unit of measurement.

[[$ 4 \cdot 2 = 8 $]] of such small cubes fit on the bottom of a right polyhedron, and three such layers are formed. This means that a total of [[$ 3\cdot 8 = 24 $]] such cubes can fit inside the polyhedron. Thus, the volume of a right polyhedron is obtained by calculating the product of its base area and height.

The unit of volume is thus [[[$ V $]]​] = [[[$ a $]]​][[[$ b $]]​][[[$ c $]]​] = cm · cm · cm = cm[[$ ^3 $]]​.

Units of volume

Volume units are the third powers or cubes of length units. The length dimension ratio is [[$ 10 $]], which means that the volume dimension ratio must be [[$ 10\cdot10\cdot10= 1,000 $]]. Thus, when moving to the next unit of measurement, the position of the comma must be moved by three steps.

unit	name	in base units
mm[[$ ^3 $]]​	cubic millimeter	[[$ 0,000000001 $]]​ m[[$ ^3 $]]​
cm[[$ ^3 $]]​	cubic centimeter	[[$ 0,000001 $]]​ m[[$ ^3 $]]​
dm[[$ ^3 $]]​	cubic decimeter	[[$ 0,001 $]]​ m[[$ ^3 $]]​
m[[$ ^3 $]]​	cubic meter	[[$ 1 $]]​ m[[$ ^3 $]]​

Litres

Liter units are used to express volumes of liquid substances. The ratio of consecutive liter units is [[$ 10 $]]. Therefore, when moving to the next liter unit, only one step needs to be moved.

symbol	name	in base units
ml	milliliter	[[$ 0,001 \; \text {l} $]]​
cl	centiliter	[[$ 0,001 \;\text {l} $]]​
dl	deciliter	[[$ 0,01 \;\text {l} $]]​
l​	liter	[[$ 1 \;\text {l} $]]​

Volume and litre units have corresponding units, for example [[$ 1 \;\text {liter} = 1 \;\text {dm}^3 $]]​.

Example 1

Convert [[$ 540 000 000 $]]​ mm[[$ ^3 $]]​ into cubic meters.

​[[$ 540\;000\;000 \;\text {mm}^3 = 540\;000 \;\text {cm}^3 \\ 540\;000 \;\text {cm}^3 = 540 \;\text {dm}^3 \\ 540 \;\text {dm}^3 = 0,54 \;\text {m}^3 \\ $]]​

Answer: [[$ 540\;000\;000 \;\text{mm}^3 $]]​ is equal to[[$ 0,54 \;\text m^3 $]]​.

Example 2

Convert [[$ 0,55 $]]​ litres into cubic centimeters.

[[$ 0,55 \;\text{l} = 0,55 \;\text{dm}^3 = 550 \;\text{cm}^3 $]]​

Answer: [[$ 0,55 $]] ​litres is [[$ 550 \;\text{cm}^3 $]]​.