Answer with explanation:
Since the density of the rocks at the surface of earth equals [tex]2-4gm/cm^{3}[/tex] which is much lesser than the average density of the earth equaling [tex]5.5gm/cm^{3}[/tex] thus we conclude the density of material closer is greater than [tex]5.5gm/cm^{3}[/tex].This can be mathematically shown as under:
[tex]\rho _{earth}=\frac{\rho _{surface}+\rho _{core}}{2}\\\\5.5gm/cm^{3}=\frac{(2-4)gm/cm^{3}+\rho _{core}}{2}\\\\\therefore \rho_{core}=[2\times 5.5-(2-4)]gm/cm^{3}\\\\\therefore \rho_{core}=(7-9)gm/cm^{3}[/tex]
Thus we conclude that the density of the matter closer to the center ranges between [tex]7-9gm/cm^{3}[/tex]
