(a) One solar mass is equal to [tex]2\cdot 10^{30}kg[/tex], so the mass of the neutron star is 1.5 times this value:
[tex]M=1.5 M_s =1.5 \cdot 2\cdot 10^{30}kg=3\cdot 10^{30}kg[/tex]
The radius of the star is [tex]r=10 km=10000 m[/tex], so its volume is
[tex]V= \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (10000 m)^3 = 4.2 \cdot 10^8 m^3 [/tex]
So, the density of the neutron star is
[tex]d= \frac{M}{V} = \frac{3 \cdot 10^{30}kg}{4.2 \cdot 10^8 m^3}=7.1 \cdot 10^{21} kg/m^3 [/tex]
(b) We want to find the mass of 1 cm^3 of neutron star. The volume is
[tex]V=1 cm^3 = 1 \cdot 10^{-6}m^3 [/tex]
so, by using the density we found at point (a), we can calculate the mass of 1 cm^3 of neutron star:
[tex]m=dV=(7.1 \cdot 10^{21}kg/m^3)(1 \cdot 10^{-6}m^3)=7.1 \cdot 10^{15} kg[/tex]
So, 1 cm^3 of neutron star has more mass than Mt Everest (whose mass is [tex]5 \cdot 10^{10}kg[/tex]).
