$6\mathrm{.}28$ A proposed grading plan requires $223,120m^3$ of cut and $206,670m^3$ of fill. Laboratory

tests on a series of undisturbed samples from the cut area produced the following results:

A series of modified Proctor tests on representative bulk samples produced a maximum

dry unit weight of $19\mathrm{.}2k\frac{N}{m^3}$ and an optimum moisture content of $10\mathrm{.}2\%.$ The project

specifications require a relative compaction based on the modified Proctor test of at least

$90\%.$

$($a$)$ Determine the shrinkage factor and compute the required volume of import or

export, if any. Use the dry unit weight of the cut when computing any import or

export quantities.

$($b$)$ Determine the weight of any import or export soil, assuming it has a moisture

content equal to the average moisture content in the cut. Express your answer in

metric tons $(1$ metric ton $=1000kg=1Mg).$