Question

Calculate the mass of $8{m^3}$ of cement of density $2000\,\,kg/{m^3}.$

Answer 1

Hint: As in the question, we were given with density and volume of cement. So, to find mass of cement, dependence of mass on volume and density is to be used.
Density $ = \dfrac{{Mass}}{{Volume}}$

Complete step by step answer:
We know that the density of any sustain is mass per unit volume.
So, Density $ = \dfrac{{Mass}}{{Volume}}$
$ \Rightarrow $Mass $ = $Density $ \times $ Volume
Now, In order to find mass of cement, we are given with
Density of cement $ = 2000\,\,kg/{m^3}$
Volume of cement $ = 8\,\,{m^3}$
Hence, Mass $ = $Density $ \times $ Volume
$ = 2000 \times 8$
$ = 16000\,\,kg$

Additional Information:
$ \to $ The term density is generally denoted by the symbol $`\rho '$
i.e. \[\rho = \dfrac{m}{V}\]
Where m is mass and v is volume.
$ \to $Different substances have different densities.
$ \to $ To simplify, it is sometimes replaced by a dimensionless quantity i.e. “relative density” or “specific gravity”.
$ \to $ “Relative density or “specific gravity” is the density of any substance with respect to that of water. It is the ratio of density of substances to the density of water.
$ \to $ The density of a material varies with temperature and pressure.
$ \to $ Density is an intensive property i.e. increasing the amount of any substances does not increase its density. Rathes, it increases its mass.
$ \to $ It is units in the SI system are \[kg\, - {m^{ - 3}}\] and in cgs are $g\, - c{m^{ - 3}}$.
$ \to $ It is dimensional formula is $\left[ {M{L^{ - 3}}} \right].$

Note:
So, mass of cement is $16000\,\,kg$ one can also solve this question by unitary method which is
As density $ = 2000\,\,kg/{m^3}$
This states that,
Mass of $1\,\,{m^3}$ of cement $ = 2000\,\,kg$
Mass of $8\,\,{m^3}$ of cement $ = 2000 \times 8\,\,kg$
$ = 16000\,\,kg$.