How Much Does Earth's Atmosphere Weigh?

[nikita33]

Homework Statement

above each square inch of Earth's surface is 14.7 lbs of air. the density of air at sea level is about 1.27g/L. the Earth is 7930 miles in diameter and has a mass of 5.98 x 10^24kg.
a.) use the data above to determine the mass in kg of the Earth's atmosphere.

b.) determine the average density of Earth in grams per milliliter.

Homework Equations

i think the only relevant equation is d=m/v. everything else seems to be unit conversions. this problem really isn't about the atmosphere, but rather how well i can convert units, and apparently not well.

The Attempt at a Solution

im looking for the mass of the atmosphere, so i use m = dv
d is 1.27g/mL
i derive v from 4/3pir^3
but i have the radius in miles. does this matter?
i would get (1.27g/mL)(2.55x10^11) since i need it in kg
(1.27 x 10^-3kg)(2.55x10^11) = 3.24 x 10^8 kg/mL?

im sure I am hopelessly wrong. i don't really want to do part b until i get part a.

 

[Redbelly98]

(a) We're given that there are 14.7 pounds of air per square inch of Earth's surface area. If you can figure out how many square inches of surface area the Earth has, can you take it from there?

(b) The equation you had, d=m/v, applies here.