During a compaction test in the lab a cylindrical mold with a diameter of $4$ in and a

height of $4\mathrm{.}58$ in was filled. The compacted soil in the mold weighted $41$ lb and had a

moisture content of $12\%.$ If the specific gravity is $2\mathrm{.}72,$ determine:

a$)$ dry unit weight

b$)$ void ratio

c$)$ degree of saturation

d$)$ additional water $($in lb$)$ needed to achieve $100\%$ saturation in the soil sample