Explanation:
It is given that,
Density of asteroid, [tex]\rho=4000\ kg/m^3[/tex]
Mass of asteroid, [tex]m=10^{17}\ kg[/tex]
We need to find the diameter of the asteroid. The formula of density is given by:
[tex]\rho=\dfrac{m}{V}[/tex]
V is the volume of spherical shaped asteroid, [tex]V=\dfrac{4}{3}\pi r^3[/tex]
[tex]r^3=\dfrac{3M}{4\pi \rho}[/tex]
[tex]r^3=\dfrac{3\times 10^{17}\ kg}{4\pi \times 4000\ kg/m^3}[/tex]
[tex]r^3=\sqrt{5.96\times 10^{12}}[/tex]
r = 2441311.12 m
Diameter = 2 × radius
d = 4882622.24 m
or
[tex]d=4.88\times 10^6\ m[/tex]
Hence, this is the required solution.