Question

Estimate the mass of water on earth. The density of water is 1000kgm-³.Give answer to 1 significant figure.

Answer 1

We happen to know the deepest points in the ocean are around 10 km and that it is not uncommon for the ocean to be deeper than 1 km, so we take the average depth to be around

$$D=\sqrt{10^4(10^3)}=3\cdot10^3\ m$$

We estimate the surface area of Earth (and hence the surface area of Earth’s oceans) to be roughly

$$A=\pi d^2=\pi (10^7)^2=3\cdot10^{14}\ m^2$$

$$V=AD=(3\cdot10^{14})(3\cdot10^{3})=9\cdot10^{17}\ m^3$$

$$m=\rho V=9\cdot10^{17}(10^3)=9\cdot10^{20}\ kg$$