Question

Calculate the mass of air enclosed in a room of length, breadth and height equal to $5m,3m$and $4m$respectively. Density of air is$1.3kg/{m^3}$.
A. $78kg$
B. $38kg$
C. $42kg$
D. $87kg$

Answer 1

Hint: As in the question, we are given density and to calculate mass from it, volume is required. So, by finding the volume of the room and then density dependence on mass and volume, the mass of air enclosed in the room can be calculated.

Formula used:
(1) Volume of room $ = $ lbh
Where l is length, b is breadth, and h is height
(2) Density $ = \dfrac{{Mass}}{{Volume}}$
$ \Rightarrow mass = density \times volume$

Complete step by step answer:
We know that the shape of the room is cuboidal with
Length (l) $ = 5m$
Breadth (b) $ = 3m$ and height (h) $ = 4m$
The volume of air enclosed in room
$ = $ Volume of the room
$ = $ Volume of cuboid
$
   = lbh \\
   = 5 \times 3 \times 4 \\
  60{m^3} \\
 $
So, volume of air enclosed in room
$ = 60{m^3}$
So, volume of air enclosed in room $ = 60{m^3}$
Now, as density is mass per unit volume
So, mass of air $ = \left( {volume \times density} \right)$of air
Mass of air$ = 60{m^3} \times 1.3kg/{m^3}$
Mass of air $ = 78kg$
So, mass of air enclosed in room is $78kg$

So, the correct answer is “Option A”.

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 hot water. It is the ratio of density of substance 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 substance does not increase its density. Rather, it increases its mass.
$ \to $ Its units in SI system are $kg - {m^{ - 3}}$ and in CGS are $g - c{m^{ - 3}}$
$ \to $ Its dimensional formula is $\left[ {M{L^{ - 3}}} \right]$

Note:
This can also be solved by unitary method which is mass of air corresponding to $1{m^3} = 1.3kg$
Mass of air corresponding to $60{m^3}$
$
   = 60 \times 1.3 \\
   = 78kg. \\
 $