Question $1(20$ marks$)$:

The hollow$-$stem auger is used to dig a borehole in the ground and rotated to dig down to the

desired depth of $2$ m below the ground surface. The driller removes the temporary plug and inserts

the split$-$barrel sampler through the stem. The split$-$barrel sampler retrieves a cylindrical shape soil

sample with a diameter of $50$ mm and a length of $0\mathrm{.}5$ m $.$ The weight of the collected soil sample is

$1\mathrm{.}750$ kg and its moisture content is $20\%.$ Considering a reasonable value for the specific gravity

of solids, compute:

a$)(5$ marks$)$ degree of saturation,

b$)(5$ marks$)$ porosity,

c$)(5$ marks$)$ saturated unit weight, and

d$)(5$ marks$)$ dry unit weight.