$[10]1.$ A Modified Proctor compact test is performed on a soil sample. In one of the compaction trials, the following was obtained: Total mass of the soil in the compaction mold: $2092$ g

Total volume of mold: $944c{m}^3$

To determine the water content of the soil for this trial, the following was measured:

Mass of tare: $24\mathrm{.}50$ g $.$ Mass of wet soil $+$ tare: $57\mathrm{.}41g,$ Mass of dry soil $+$ tare: $53\mathrm{.}19$ g

$($a$)$ Determine the water content of the soil for this trial.

$($b$)$ Determine the total mass density of the soil in $\frac{g}{c}{m}^3.$

$($c$)$ Determine the dry mass density ${}_d$ of the soil in $\frac{g}{c}{m}^3.$

$($d$)$ Assuming $Gs=2\mathrm{.}67,$ what is the void ratio $e?$