$12\mathrm{.}2$ A cube $5\mathrm{.}0$ cm on each side is made of a metal alloy. After you drill a cylindrical hole $2\mathrm{.}0$ cm in diameter all the way through and perpendicular to one face, you find that the cube weighs $6\mathrm{.}30$ N$.($a$)$ What is the density of this metal? $($b$)$ What did the cube weigh before you drilled the hole in it$?$