Question

Determine the density of the earth assuming the earth is sphere. Take the radius of the earth r=6.37×10^6

And the mass of the earth m=5.98×10^24

Show your work

Answer 1

By definition, the density is:

$$\rho = \dfrac{m}{V}$$

where $m = 5.98\times 10^{24}kg$ is the mass of the Earth, and $V$ is its volume. Considering the Earth to be a ball with radius $r = 6.67\times 10^6m$, the volume is:

$$V = \dfrac{4}{3}\pi r^3$$

Thus, the density will be:

$$\rho = \dfrac{3m}{4\pi r^3}\\ \rho = \dfrac{3\cdot 5.98\times 10^{24}}{4\pi (6.67\times 10^6)^3} \approx 4.81\times 10^3\space \dfrac{kg}{m^3}$$

Answer. $4.81\times 10^3\space \dfrac{kg}{m^3}$