Question

One litre of water weighs 1kg. How many cubic millimetres of water will weigh 0.1 gram?
(a)100 cubic mm
(b)150 cubic mm
(c)90 cubic mm
(d)80 cubic mm

Answer 1

Hint: It is given in the question that 1 litre of water weighs 1kg or 1 litre of water weighs 1000g. Convert 1 litre into the units of millimeters. We know that 1 litre is equal to 1000 millilitres and 1 millilitre is equal to $1c{{m}^{3}}$ and $1cm=10mm$ so $1c{{m}^{3}}=1000m{{m}^{3}}$.Now, substituting millilitres in terms of $m{{m}^{3}}$ we get $1litre=1000\left( 1000m{{m}^{3}} \right)$ or we can write $1litre={{10}^{6}}m{{m}^{3}}$.Rephrasing the statement 1 litre of water weighs 1000g as ${{10}^{6}}m{{m}^{3}}$ of water weighs 1000g so 100 cubic millimeters of water weighs 0.1g.

Complete step-by-step answer:
It is given that one litre of water weighs 1kg.
We know that $1kg=1000g$ so rephrasing the above statement,
One litre of water weighs 1000g.
Now, we need the answer in cubic millimeters for that we have to convert the units of litre into cubic millimeters.
We know that,
$1litre=1000mL$…….. Eq. (1)
And converting millilitre (mL) to $c{{m}^{3}}$ we get,
$1mL=1c{{m}^{3}}$
Substituting mL to $c{{m}^{3}}$ in eq. (1) we get,
$1litre=1000c{{m}^{3}}$ …………… Eq. (2)
We know that,
$1cm=10mm$
Cubing on both the sides we get,
$1c{{m}^{3}}=1000m{{m}^{3}}$
Substituting $m{{m}^{3}}$ in place of $c{{m}^{3}}$in eq. (2) we get,
$\begin{align}
  & 1litre=1000\left( 1000m{{m}^{3}} \right) \\
 & \Rightarrow 1litre={{10}^{6}}m{{m}^{3}} \\
\end{align}$
It is given that 1 litre of water weighs 1000g or from the above conversion, we can say that ${{10}^{6}}m{{m}^{3}}$ of water weighs 1000g.
The volume of 1000g water = ${{10}^{6}}m{{m}^{3}}$
The volume of 1g of water = $\dfrac{{{10}^{6}}}{1000}=1000m{{m}^{3}}$
So, the volume of 0.1g of water = $1000\left( 0.1 \right)=100m{{m}^{3}}$
From the above solution we get that $100m{{m}^{3}}$ of water weighs 0.1g.
Hence, the correct option is (a).

Note: Don’t confuse “millimetres” given in the question to “millilitres”. Generally, in the hastiness of solving the problem in exams people tend to make such mistakes.
Be careful while making the conversions from litre to millimetres, mistakes could happen in the zeros.