$($a$)$ In a cone penetration test on a cohesive fine$-$grained soil sample, the following results were recorded:

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Test & $\backslash$begin$\{$tabular$\}\{$c$\}$

Mass of $\backslash \backslash$

container $\backslash \backslash$

$\backslash ((\backslash$mathrm$\{$g$\})\backslash )$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Mass of wet soil $\backslash \backslash$

$\backslash$& container $\backslash \backslash$

$\backslash ((\backslash$mathrm$\{$g$\})\backslash )$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Mass of dry soil $\backslash \backslash$

$\backslash$& container $\backslash \backslash$

$\backslash ((\backslash$mathrm$\{$g$\})\backslash )$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Average cone $\backslash \backslash$

penetration $\backslash \backslash$

$\backslash ((\backslash$mathrm$\{$mm$\})\backslash )$

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline $1$ & $16\mathrm{.}55$ & $34\mathrm{.}94$ & $30\mathrm{.}27$ & $17\mathrm{.}7\backslash \backslash$

$\backslash$hline $2$ & $15\mathrm{.}77$ & $29\mathrm{.}82$ & $26\mathrm{.}16$ & $18\mathrm{.}5\backslash \backslash$

$\backslash$hline $3$ & $15\mathrm{.}88$ & $29\mathrm{.}18$ & $25\mathrm{.}51$ & $22\mathrm{.}6\backslash \backslash$

$\backslash$hline $4$ & $16\mathrm{.}61$ & $29\mathrm{.}72$ & $26\mathrm{.}02$ & $23\mathrm{.}3\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Table Q$3$

Find, graphically, the liquid limit of the soil sample. $($Note: You may use Excel's Trendline $($Linear$)$ to plot graph for this assignment question.$)$

$($b$)$ Calculate the plasticity index if the plastic limit was $\backslash (21\backslash \%\backslash ).$

$($c$)$ What is the classification of this soil sample according to the plasticity chart?

riastic$$ty Lnart