Question

Mass of oil is \[11040\,{\text{kg}}\] and volume is \[{\text{12 }}{{\text{m}}^3}\], its density would be:
A. \[92\,{\text{kg}}{{\text{m}}^{{\text{ - 3}}}}\]
B. \[920\,{\text{kg}}{{\text{m}}^{{\text{ - 3}}}}\]
C. \[9.2\,{\text{kg}}{{\text{m}}^{{\text{ - 3}}}}\]
D. \[1.08\,{\text{kg}}{{\text{m}}^{{\text{ - 3}}}}\]

Answer 1

Hint:We are asked to find the density of oil whose mass and volume are given. First, understand the meaning of density and try to write the mathematical form of density in terms of mass and volume. Then put the values of mass and volume given to calculate the value of density of the oil.

Complete step by step answer:
Given, mass of oil, \[m = 11040\,{\text{kg}}\].Volume of the oil, \[V = {\text{12 }}{{\text{m}}^3}\]. To find the density, we first understand what is meant by density. Density of a material can be defined as mass per unit volume that is in mathematical form we can write density as,
\[\rho = \dfrac{{{\text{Mass}}}}{{{\text{Volume}}}}\] (i)
Here, the mass is \[m = 11040\,{\text{kg}}\] and the volume is \[V = {\text{12 }}{{\text{m}}^3}\].
Putting these values in equation (i) we get,
\[\rho = \dfrac{{11040\,{\text{kg}}}}{{{\text{12 }}{{\text{m}}^3}}}\]
\[ \therefore \rho = 920\,{\text{kg}}{{\text{m}}^{ - 3}}\]
Therefore, the density of the oil will be \[920\,{\text{kg}}{{\text{m}}^{ - 3}}\].

Hence, the correct answer is option B.

Note: In such types of questions, before proceeding for calculations first check the units of the given quantities whether the units of the given quantities are the same, that is all are in SI unit or in CGS unit. For example here the mass of oil was given in SI unit that is in kilogram but if it was given in CGS unit that is gram and volume given in SI unit then we would first need to convert the mass into SI unit and then proceed for calculation. One important point to remember about density is that, density decreases with increase in volume and increases with increase in mass.