Question

1 litre = _____________ $c{{m}^{3}}$
A. ${{10}^{6}}$
B. ${{10}^{5}}$
C. 1
D. ${{10}^{3}}$

Answer 1

Hint: You may recall that the physical quantity that is measured in the above given units is volume. You may then think of the SI unit of volume. Then you may be able to relate the given units to this SI unit in case if you don’t know the direct conversion. Thereby you will be able to get the answer.

Complete step by step answer:
In the question, we are asked to convert 1Litre into centimeter cube. You may recall that both these units are that of volume. The SI unit of volume is actually cubic meter$\left( {{m}^{3}} \right)$.
Volume of an object could be defined as the amount of space that particular object occupies in space. Consider a cube of edge length L of 1m, then, the volume occupied by that cube in space can be given by,
$V=L\times L\times L={{L}^{3}}\sim {{m}^{3}}$
Also, we know that 1 cubic meter is equivalent to one litre. So, we have,
$1{{m}^{3}}=1Litre$ ……………………………………… (1)
You may recall that centi is a prefix added to meter and 1cm can be said to be equivalent to,
$1cm={{10}^{-2}}m$
$\Rightarrow 1m={{10}^{2}}cm$
Now, on cubing both sides we will get,
$1{{m}^{3}}={{\left( {{10}^{2}} \right)}^{3}}c{{m}^{3}}$
Now, from equation (1) we have,
$\therefore 1Litre={{10}^{6}}c{{m}^{3}}$
So, we finally found that 1Litre = ${{10}^{6}}c{{m}^{3}}$

So, the correct answer is “Option A”.

Note: Though we have taken the case of a cube for easy reference all the above units apply to other 3-dimensional objects. We have other prefixes that we use in units like milli, micro, nano, pico, etc. Litre is the most commonly used unit for volumes of which you may be very familiar. The SI unit system is based on 7 fundamental units.