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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
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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 1cm3 and 1cm=10mm so 1cm3=1000mm3.Now, substituting millilitres in terms of mm3 we get 1litre=1000(1000mm3) or we can write 1litre=106mm3.Rephrasing the statement 1 litre of water weighs 1000g as 106mm3 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 cm3 we get,
1mL=1cm3
Substituting mL to cm3 in eq. (1) we get,
1litre=1000cm3 …………… Eq. (2)
We know that,
1cm=10mm
Cubing on both the sides we get,
1cm3=1000mm3
Substituting mm3 in place of cm3in eq. (2) we get,
1litre=1000(1000mm3)1litre=106mm3
It is given that 1 litre of water weighs 1000g or from the above conversion, we can say that 106mm3 of water weighs 1000g.
The volume of 1000g water = 106mm3
The volume of 1g of water = 1061000=1000mm3
So, the volume of 0.1g of water = 1000(0.1)=100mm3
From the above solution we get that 100mm3 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.
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