A large warehouse project requires $30,000$ cubic yards of excavation $($cut$)$ and $24,000$

cubic yards of fill. The in situ soil density is $109$ pcf$,$ and the in situ water content is $14\%.$

The fill soil is to be compacted to $90\%$ relative compaction, and its maximum dry density

is $126$ pcf $($assume the fill has a uniform dry density that is $90\%$ of the maximum$).$

a$.$ Determine how much excess cut$/$fill soil the project will generate. Report your

answer as a mass of solids.

b$.$ When soil is placed in a dump truck for transportation it takes up $25\%$ more

volume than it does in situ. If a dump truck can transport $20$ cubic yards of soil

per trip, how many trips will be needed to remove all of the cut soil?

c$.$ During transportation, the cut soil loses moisture such that it arrives at the fill area

with a moisture content of $10\%.$ If the soil is to be compacted at a moisture

content of $16\%,$ how much water will need to be added to the soil to compact the

entire fill area?