A soil sample has a total density of $1\mathrm{.}82M\frac{g}{m^3}$ and loses $15\%$ of its weight upon oven drying at $100C$ for $24hrs.$ Assuming the specific gravity of the soil as $2\mathrm{.}6,$ draw the phase diagram and calculate the following.

$($i$)$ Dry density

$($ii$)$ Void ratio

$($iii$)$ Porosity

$($iv$)$ Degree of saturation

$($v$)$ Saturated density

$($vi$)$ Water content at $100\%$ saturation