a) [tex]48000 m^3[/tex]
The volume of the sports hall can be calculated using the equation
[tex]V=a\cdot b \cdot c[/tex]
where
a, b, c are the measures of the sizes of the hall
For the sport hall in this problem, we have
a = 80 m
b = 40 m
c = 15 m
Substituting into the equation, we find
[tex]V=(80)(40)(15)=48,000 m^3[/tex]
b) [tex]62400 kg[/tex]
Being a gas, the air fills the whole sport halls, therefore its volume is equal to the volume of the sports hall.
The relationship between the mass, the volume and the density of the air is
[tex]\rho = \frac{m}{V}[/tex]
where
[tex]\rho[/tex] is the density
m is the mass
V is the volume
Here we have:
[tex]\rho = 1.3 kg/m^3[/tex]
[tex]V=48000 m^3[/tex]
Solving for m, we find the mass of air:
[tex]m=\rho V = (1.3)(48000)=62,400 kg[/tex]
