If the radius of the Earth is $6400.0 \mathrm{~km}$ and the atmosphere is $10.0 \mathrm{~km}$ high, then the volume of air around the Earth is
A) $5.16 \times 1018 \mathrm{~m} 3$.
B) $5.2 \times 1018 \mathrm{~m}^{3}$.
C) $5.1552 \times 10^{9} \mathrm{~m}^{3}$
D) $3.605 \times 10^{16} \mathrm{~m}^{3}$.

Question

Quizplus · Accepted Answer

The volume of air around the Earth can be calculated as the difference between the volume of a sphere with radius $r_1 = 6410.0 \, \text{km}$ (Earth's radius plus the atmosphere) and the volume of a sphere with radius $r_2 = 6400.0 \, \text{km}$ (just the Earth's radius). The formula for the volume of a sphere is $\frac{4}{3}\pi r^3$. Therefore, the volume of air is $\frac{4}{3}\pi (6410^3 - 6400^3)$ cubic kilometers, which converts to approximately $5.16 \times 10^{18}$ cubic meters when calculated and converted to cubic meters.

If the Radius of the Earth Is 6400.0 km6400.0 \mathrm{~km}6400.0 km And the Atmosphere Is

If the Radius of the Earth Is $6400.0 \mathrm{~km}$ And the Atmosphere Is