What is the volume of the Earth's breathable atmosphere in square meters?

Answer 1

Assume radius of earth = 6378 km
Assume 5 km of breathable air.
Assume radius to top of atmosphere = 67383 km

To get the volume of a shell around the earth.

Subtract the volume of the earth sphere:
(pi*r^3) = 3.14159*(6,378)^3

From the volume of the "atmosphere sphere."

(3.14159*(6,7383)^3) - (3.14159*(6,378)^3)
= approx. 1,918,448,800 cubic km
.

Answer 2

Square meters is area, not volume

Here is some stuff I did recently, hope u can follow it and it helps you to understand:


4*pi*R^2 = (4)(3.14159)(4000)^2 = (12.57)(16000000) = 201,061,929.83 square miles of earths surface

one square mile = 5280^2 square feet = 27,878,400 square feet (IE square feet in a square mile)

one square foot = 12^2 square inches = 144 square inches (IE square inchws in a square foot)

Atmosphere per square inch = 14.7 pounds (lbs)

Multiplying these four numbers together will give the total weight of the earth's atmosphere

(201,061,929.83)(27,878,400)(144)(14.7) = 11,865,267,085,999,432,089.2 pounds

Dividing by 2000 converts this to tons 5,932,633,542,999,716 tons of air on earth

Dividing by 6,500,000,000 (population of earth) yields 912,712 tons of air per person

An adult breathes about 35 pounds of air per day so the 912,712 tons will last you

about 52 million days or 142,000 years.

Volume of atmosphere per capita (calculated at 13 cu ft air = 1 lb)

(912,712)(2000)(13) = 23,730,512,000 cubic feet of atmosphere per person

(14.7)(13) = 191.1 cu ft of atmos / sq in earth surface

(191.1)(144) = 27,518.4 feet height of atmosphere per sq inch earth's surface (if a constant density)

27,518.4/5280 = 5.212 miles height std atmosphere (air at 13 lbs/ ft^3 to create 14.7 psi)