$3,4$ During a compaction test in the geotechnical laboratory, the students compacted a clayey soil into a cylindrical mold $4$ in$.$ in diameter and $4\mathrm{.}58$ in$.$ in height. The compacted soil in the mold weighed $4lb,$ and it had a moisture content of $12\%.$ If $G_s=2\mathrm{.}72,$ determine the following:

a$.$ Dry unit weight

b$.$ Void ratio

c$.$ Degree of saturation

d$.$ Additional water $($in th$)$ needed to achieve $100\%$ saturation in the soll sample