Question

Given, $1\text{ liter = }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ }\!\!\_\!\!\text{ c}{{\text{m}}^{3}}$
A. 100
B. 1000
C. 10
D. 1

Answer 1

Hint: Define unit system and how we can use different units to express the same quantity. 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 a cubic box of side 10 cm..

Complete step by step answer:
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
$V={{1}^{3}}{{m}^{3}}=1{{m}^{3}}$
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,
$\begin{align}
  & 1L=10cm\times 10cm\times 10cm \\
 & 1L=1000c{{m}^{3}} \\
\end{align}$
So, the correct option is (B)

Additional information:
From the above we can write that,
$1c{{m}^{3}}=\dfrac{1}{1000}L$
We can express the ${{m}^{3}}$ in terms of litre as,
$\begin{align}
  & 1{{m}^{3}}=1m\times 1m\times 1m \\
 & 1{{m}^{3}}=100cm\times 100cm\times 100cm \\
 & 1{{m}^{3}}=1000000c{{m}^{3}} \\
 & 1{{m}^{3}}=1000000\times \dfrac{1}{1000}L \\
 & 1{{m}^{3}}=1000L \\
\end{align}$
So, in the SI unit system we define the unit of volume as ${{m}^{3}}$ which is equal to 1000 L.

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.