Consider a lagoon that can be modeled as a perfect hemisphere $($half of a sphere$)$ having a diameter of $50m.$ If river water flows into and out of the reservoir at $7\mathrm{.}5\frac{m^3}{m}in,$ calculate the residence$/$retention time of the lagoon in days.

$[$Hint: Volume of a sphere is $(\frac{4}{3})r^3]$