$5(14)$A lighter$-$than$-$air spherical balloon and its load of passengers and ballast are floating stationary above the earth. Ballast is weight $($of negligible volume$)$ that can be dropped overboard to make the balloon rise. The diameter of this balloon is $5\mathrm{.}35$ m$.$ Assuming a constant value of $1\mathrm{.}29$ kg$/$m$3$ for the density of air, determine how much weight must be dropped overboard to make the balloon rise $167$ m in $14$

$\mathrm{.}0$ s$.$