A barge with an approximately rectangular cross$-$section carries grain from a river. The barge has a width of $8\mathrm{.}5$ m and a length of $27\mathrm{.}5$ m$.$ The odd number $($submerged depth$)$ of unloading grain is $1\mathrm{.}5$ m$,$ and the number of days of loading cargo is $2\mathrm{.}1$ m$.($a$)$ Find the weight of the barge that has been unloaded. $($b$)$ Find the weight of the grain.