Answer: [tex]5.935(10)^{13}g/cm^{3}}[/tex]
Explanation:
Density is a characteristic property bodies and materials, and is defined as the relationship between the mass [tex]m[/tex] and the volume [tex]V[/tex], as shown below:
[tex]D=\frac{m}{V}[/tex] (1)
In the case of the neutron star, we know it has the same mass as the Sun:
[tex]m=1.989(10)^{30}kg[/tex]
And its radius is [tex]r=20km[/tex]
On the other hand, if we assume this neutron star has a spherical shape, its volume can be calculated by the following formula:
[tex]V=V_{sphere}=\frac{4}{3}\pir^{3}[/tex] (2)
[tex]V=\frac{4}{3}\pi(20km)^{3}[/tex] (3)
[tex]V=33510.321km^{3}[/tex] (4)
Substituting (4) in (1):
[tex]D=\frac{1.989(10)^{30}kg}{33510.321km^{3}}[/tex] (5)
Finally:
[tex]D=5.935(10)^{25}kg/km^{3}}=5.935(10)^{13}g/cm^{3}}[/tex]
