Question

What is the SI unit of volume? How is it related to litre?

Answer 1

Hint: SI units are standard units of measurement defined by the international convention. Define what is volume and how we can measure it. Find the SI unit of volume. Obtain the conversion from $c{m}^3$ to L by defining the litre as the volume occupied by the cubic box.

Complete step-by-step solution -
SI unit or International system of units is a system of units based on the metre, kilogram, second, ampere, kelvin, candela and mole. We also have a set of prefixes to indicate the multiplication and division by a power of ten.
Volume of an object can be defined as the space occupied by the object or the space contained within a container.
The SI unit of volume is cubic meter or $m^3$.
For a cube with side 1 m, the volume of the cube will be
$V=1^3{m}^3=1m^3$
A meter cube can be simply defined as the volume occupied by a cube of side one meter each.
The litre (L) can be defined as the volume of a cube with side 10 cm each.
So, we can mathematically write that,
$\begin{array}{rl}& 1L=10cm\times 10cm\times 10cm\\ & 1L=1000c{m}^3\end{array}$
From this we can write that,
$1c{m}^3={\displaystyle \frac{1}{1000}}L$
We can express the $m^3$ in terms of litre as,
$\begin{array}{rl}& 1m^3=1m\times 1m\times 1m\\ & 1m^3=100cm\times 100cm\times 100cm\\ & 1m^3=1000000c{m}^3\\ & 1m^3=1000000\times {\displaystyle \frac{1}{1000}}L\\ & 1m^3=1000L\end{array}$

Note: Dimension of volume is $$\left[L^3\right]$$
Volume can be defined as the amount of space that an object occupies. It is determined by other measurements of length which is a fundamental quantity. So, it is called a derived unit. Barrels, bushels, drams, gills, pecks, teaspoons, cubic inch, cubic foot and other units are used in the empirical system. Cubic metre, litre, cubic centimetre and other units are used in SI systems.