Question

One litre of water weighs 1 kg. How many cubic millimeters 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: First of all this is a very simple and a very easy problem. This problem deals with meter to millimeter conversion and kilograms to grams conversion and at last cubic centimeter to cubic millimeter conversion.
The litre conversion is as given below:
1 litre is equal to a thousand milliliters, as given below:
$\Rightarrow$1L = 1000 ml.
1 kilogram is equal to a thousand grams, as given below;
$\Rightarrow$1Kg = 1000 g.

Complete step-by-step answer:
Given that one litre of water weighs 1 kilogram.
Also given that some amount of cubic millimeters of water weighs 0.1 grams.
We have to find the amount of cubic millimeters of water that weighs 0.1 grams.
Given that one litre of water weighs 1 kg, which is expressed as below:
$\Rightarrow 1L\to 1Kg$
Which means that thousand millilitres of water weighs a thousand grams, which is expressed below;
$\Rightarrow 1000ml\to 1000g$
Which further implies on simplification, as given below:
$\Rightarrow 1ml\to 1g$
That is one millilitre of water weighs one gram.
Hence 0.1 grams of weight of water should contain 0.1 millilitre, as given below:
$\Rightarrow 0.1g\to 0.1ml$
As it is asked in cubic millimeters, therefore multiplying 0.1 millilitre with ${10}^3$, as given below;
$\Rightarrow 0.1\times {10}^3=100$cubic mm.
$\therefore$100 cubic millimeters of water will weigh 0.1 gram.

100 cubic mm of water will weigh 0.1 gram.

Note:
While solving this problem we need to understand that the litre conversion is very important and is very crucial in real life applications.
The most important conversion in the problem is that one litre is a thousand cubic cm of water, as given below:
$\Rightarrow 1L=1000$cubic cm of water that weighs 1000 grams. Hence it is converted accordingly to solve the problem
Here are some conversions that we need to remember always, which are given below:
$\Rightarrow 1$Litre = 1000 ml , and hence 1 ml = ${10}^{-3}$Litre.
$\Rightarrow 1$Kg = 1000 g, and hence 1 g = ${10}^{-3}$kg.