$3\mathrm{.}15$ For a given sand, the maximum and minimum void ratios are $0\mathrm{.}78$ and $0\mathrm{.}43,$ respectively. Given $G_s=2\mathrm{.}67,$ determine the dry unit weight of the soil in $k\frac{N}{m^3}$ when the relative density is $65\%.$

$3\mathrm{.}16$ For a given sandy soil, $e_{\text{m}\text{a}\text{x}}=0\mathrm{.}75,e_{\text{m}\text{i}\text{n}}=0\mathrm{.}46,$ and $G_s=2\mathrm{.}68.$ What will be the moist unit weight of compaction $(k\frac{N}{m^3})$ in the field if $D_r=78\%$ and $w=9\%?$