Answer:
The mass of the asteroids is 0.000334896182184 times the mass of the Earth.
39929.4542466 m
Explanation:
Total mass of the asteroids
[tex]m_a20000\times 10^{17}=2\times 10^{21}\ kg[/tex]
[tex]m_e[/tex] = Mass of Earth = [tex]5.972\times 10^{24}\ kg[/tex]
The ratio is
[tex]\dfrac{m_a}{m_e}=\dfrac{2\times 10^{21}}{5.972\times 10^{24}}\\\Rightarrow \dfrac{m_a}{m_e}=0.000334896182184[/tex]
The mass of the asteroids is 0.000334896182184 times the mass of the Earth.
Volume is given by
[tex]V=\dfrac{m}{\rho}\\\Rightarrow \dfrac{4\pi}{3\times 8} d^3=\dfrac{m}{\rho}\\\Rightarrow d^3=\dfrac{3\times 8}{4\pi}\dfrac{m}{\rho}\\\Rightarrow d=(\dfrac{3\times 8}{4\pi}\dfrac{m}{\rho})^{\dfrac{1}{3}}\\\Rightarrow d=(\dfrac{3\times 8}{4\pi}\dfrac{10^{17}}{3000})^{\dfrac{1}{3}}\\\Rightarrow d=39929.4542466\ m[/tex]
The diameter is 39929.4542466 m
