Answer:
The mass of atmosphere equals [tex]6742.368\times 10^{15}kg[/tex]
Step-by-step explanation:
Since the earth can be assumed to be as sphere ,to calculate the mass of the atmosphere we need to calculate the volume of the atmosphere.
The volume of atmosphere can be found by subtracting the volume of earth from the volume of the sphere formed by envelop of atmosphere around the earth as indicated in the attached figure
Mathematically we have
[tex]V_{atmosphere}=V_{shell}-V_{earth}\\\\V_{atmosphere}=\frac{4\pi (R_{e}+h)^{3}}{3}-\frac{4\pi R_{e}^{3}}{3}\\\\V_{atmosphere}=\frac{4\pi }{3}((6370+11)^{3}-(6370)^{3})\\\\V_{atmosphere}=5618.64\times 10^{6}km^{3}\\\\\\V_{atmosphere}=5618.64\times 10^{15}m^{3}[/tex]\
Now since it is given that 1 cubic meter of atmosphere weighs 1.2 kilogram thus the mass of the whole atmosphere equals
[tex]Mass_{atmosphere}=1.2\times 5618.64\times 10^{15}kg\\\\Mass_{atmosphere}=6742.368\times 10^{15}kg[/tex]
