$(25$ Points$)$ A sample of clay with a moisture content of $20\%$ and a specific gravity is $2\mathrm{.}70$ is saturated. Determine the following parameters, make a logical assumption for either the initial volume of solids or total volume and work in $\frac{g}{c}{m}^3$ units:

a$.$ Total Density $(\frac{g}{c}{m}^3)$

b$.$ Dry Density $(\frac{g}{c}{m}^3)$

c$.$ Total Unit Weight $($pcf$)$

d$.$ Dry Unit Weight $($pcf$)$