QUESTION $3$

$($a$)$ Data from a standard compaction test was analysed and the following results were noted.

$\backslash$table$[[$Bulk density $(M\frac{g}{m^3}),1\mathrm{.}87,2\mathrm{.}04,2\mathrm{.}13,2\mathrm{.}20,2\mathrm{.}16,2\mathrm{.}09],[$Water content $(\%),5,8,10,13,16,19]]$

The specific gravity of the soil particle is $G_s=2\mathrm{.}70.$ Based on the given data:

i$)$ Plot the curve of dry density against water content.

ii$)$ Determine the maximum dry density and optimum water content.

iii$)$ On the same axes, plot the dry density$/$water content curves for zero and $5$ percent air voids.

iv$)$ Determine the air$-$voids content at the maximum dry density.