Best Answer:
First some formulae...

volume of sphere: V = (4/3)*pi*r^3

surface area of sphere: A = 4*pi*r^2

And one value which needs to be known...

mean radius of earth in kilometers: 6370km

Using these, we can easily calculate all of the values you wish. I will assume that by surface area, you want the surface area of the outer "shell" of that atmospheric layer. I will also assume that when you ask for the volume of an atmospheric layer, you want the volume of the layer itself, and not the volume of the entire Earth and its lower layers, plus that layer. To find that, we simply find the inner volume (Vi) of the Earth plus all the lower layers, and subtract this from the total outer volume (Vo).

----Troposphere, 15km

A = 4pi(6370km+15km)^2 = 4pi(6385km)^2 = 5.12x10^8 km^2

(512 million square kilometers)

Vo (troposphere) = (4/3)pi(6370km+15km)^3 = (4/3)pi(2.603x10^11)km^3 = 1.09x10^12 km^3

Vi (Earth) = (4/3)pi(6370km)^3 = (4/3)pi(2.585x10^11)km^3 = 1.083x10^12 km^3

Vo-Vi (troposphere-Earth) = 7.67x10^9 km^3

(7.67 billion cubic kilometers)

All of the rest can be found in this way. I'll shortcut through all of the extraneous math for the remainder of the calculations...

----Stratosphere, 50km

A = 518 million square kilometers

V = 18.0 billion cubic meters

----Mesosphere, 80km

A = 523 million square kilometers

V = 15.6 billion cubic meters

----Thermosphere, 110km

A = 527 million square kilometers

V = 15.8 billion cubic meters

----Exosphere, 1000km

A = 682 million square kilometers

V = 537 billion cubic meters

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