The Virgo Galaxy Cluster has a mass of $10^{14} M_{odot}$ and its centre is $16Mpc$ from Earth. The large elliptical galaxy $M87$ lies at the centre of the Virgo cluster. $M87$ has a supermassive black hole at it's centre with an estimated mass of $6 times 10^9 M_{odot}$. Take Hubble's constant to be $H_0=70 km s^{-1} Mpc^{-1}$.
Taking the Virgo cluster to be spherically symmetric with a radial density profile given by
$rho(r)=rho_0 (frac{r}{1Mpc})^{-2}$,
Determine the value of the constant $rho_0$ is S.I units assuming the radius of the Virgo cluster is 1Mpc.
I am confused with how to approach this question,
I know that density $rho=frac{M}{frac{4}{3} pi r^3}$, when I substitute it into the given radial density profile, the $r$ variable doesn't cancel, should I substitute the radius of the cluster into $r$? Is it really that straight forward?
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