The diameter of a circular silo is $2m$ and its height is $6m.$ It was filled with grain whose bulk and true densities are $800$ and $1200k\frac{g}{m^3}$ respectively. What will be the additional volume available if the packing density is increased to $850k\frac{g}{m^3}?$

$($a$)1\mathrm{.}10$

$($b$)1\mathrm{.}43$

$($c$)1\mathrm{.}64$

$($d$)1\mathrm{.}75$