Calculating mass of the atmosphere

[JerzeyDevil]

Homework Statement

Calculate the total atmospheric mass between 25S and 25N, between the pressure levels 300mb and 200mb. Assume the Earth is a perfect sphere.

Homework Equations

Radius of the Earth = 6378km
1 degree latitude = 111km
volume of cylinder = pi*r^2*h

The Attempt at a Solution

I have tried this solution using approximate, average heights of the 200 and 300mb pressure levels, and assuming the "band" of 25N and 25S is a cylinder. From here, I found the volume of the Earth up to 200mb and subtracted it from the volume of the Earth at 200mb, to get the volume between 200 and 300mb. However, my professor said there was a way to do this without estimating pressure heights, and I am unsure how to do this.

 

[JaredJames]

Did you get the answer to this in the end or is it still open?