Question

If the sun expanded to a radius 200 times it's present radius, what would be it's average density be in g/cm^3

Answer 1

Radius of expanded sun is $R_e=200R$

Mass of Sun is $M=1.989 × 10^{33}$ gram.

Volume of expanded Sun will be

$$V_e=\frac{4}{3}\pi R^3_e$$

Density will be,

$$\rho_e=\frac{M}{V_e}=\frac{3M}{4\pi R^3_e}\\ \rho_e=\frac{1}{200^3}\rho$$

where, $\rho$ is the density of Sun before expansion begin. Thus,

$$\rho_e=1.76\times 10^{-7}\:g/cm^3$$