Soil at a borrow pit has a bulk unit weight of $18\mathrm{.}1$ kN$/$m$3$

and water content $9\mathrm{.}5\%.$ This soil is used to construct an

embankment with a total volume of $42,000$ m$3$

$.$ The embankment will be compacted to a dry unit weight of $17\mathrm{.}1$

kN$/$m$3$ and a water content of $15\%.$ The soil is excavated form the borrow pit and placed in trucks each with capacity

$4\mathrm{.}5$ m$3$

$.$ According to the highway regulations the maximum weight carried by the truck should not exceed $67\mathrm{.}5$ kN$.$

a$.$ How many m$3$ of soil should be excavated from the borrow pit to construct the proposed embankment?

b$.$ Calculate the number of truckloads needed to complete the embankment.

c$.$ Calculate the volume of water $($in m$3$

$)$ that is required to bring the soil to the required moisture content.