$($b$)$ For a field test the technician is using a sand with a density of $92\mathrm{.}15pcf$ in his sand cone test.

Calculate the dry density, degree of saturation and moisture content of a compacted fill using the

following data that the technician collected:

Weight of sand cone bottle before test $($full of sand$)$: $13\mathrm{.}72lbs$

Final weight of sand cone $($some sand remains$)$: $4\mathrm{.}31lbs$

Weight of sand needed to fill cone: $2\mathrm{.}43lbs$

Weight of fill soil excavated from hole $+$ bucket: $10\mathrm{.}91lbs$

Weight of bucket used to collect fill soil: $0\mathrm{.}87lbs$

Moisture content of fill soil:

Empty can: $42\mathrm{.}1g$

Can $+$ moist soil: $273\mathrm{.}8g$

Can $+$ dry soil: $242\mathrm{.}2g$