A $50m$ high silo is fully loaded with $500$ tonnes of grain. The true and bulk densities of the grain are $1500$ and $450k\frac{g}{m^3},$ respectively. Calculate the diameter of the silo $($m$)$ and void fraction of grain in the silo.

$($a$)6\mathrm{.}32$ and $0\mathrm{.}9$

$($b$)5\mathrm{.}31$ and $0\mathrm{.}7$

$($c$)5\mathrm{.}31$ and $0\mathrm{.}8$

$($d$)6\mathrm{.}32$ and $0\mathrm{.}6$