How can I calculate the solar central density $\rho_C = 150 \textrm{g cm}^{-3}$ using one of the equations of stellar structure like the the mass distribution equation $\frac{dM(r)}{dr}=4 \pi r^2 \rho(r)$. This describes the mass M(r) contained within a radius r in terms of the mass density ρ (rho).]
Its not about the density at R=0, since the mass inside a sphere of radius R=0 is of course 0. But density is defined as mass per unit volume: So, you can imagine a small volume at the centre of the Sun, having mass.
