A Proctor standard compaction test was conducted on a soil sample, determining the

material had a maximum dry unit weight of $19$ kN$/$m$3$ and an optimum moisture content of $11\mathrm{.}5\%.$

In$-$situ, the material was found to have a unit weight of $17\mathrm{.}2$ kN$/$m$3$ and a water content of $8\mathrm{.}2\%.$ For

use on site, the soil must be compacted to $95\%$ of its maximum dry unit weight.

Determine:

a$.$ The volume of natural in$-$situ material needed for $0\mathrm{.}5$ m$3$ of the final constructed material

b$.$ The additional weight of water to each $0\mathrm{.}5$ m$3$ of natural material that must be added to

reach $95\%$ compaction

c$.$ How many $10$ m$3$ truckloads are needed to transport the material needed for the project,

knowing a final volume of $50,000$ m$3$ is required