Question

Estimate the mass of water on earth. The density of water is 1000kgm-³. Give ans to 1 sig fig.
Here are some approximations you can use.
Compared with oceans, lakes and rivers are tiny. Clouds have low density. There is still lots of ice in the polar regions, but much less area than in oceans.so, neglect all except the ocean which cover ⅔ of the earth.
Looking at charts of the ocean, we see that the depth is typically several thousand m ( and a serious search tells me the average depth is 4700m) the radius of the earth is 6000km. The surface area of a sphere is 4×3.14×r²

Answer 1

We estimate the surface area of Earth’s oceans to be roughly

$$A=\frac{2}{3}4\pi r^2=\frac{2}{3}4\pi (6\cdot10^6)^2=3\cdot10^{14}\ m^2$$

$$V=AD=(3\cdot10^{14})(4700)=1\cdot10^{18}\ m^3$$

$$m=\rho V=1\cdot10^{18}(10^3)=10^{21}\ kg$$