$($a$)$ A cone penetrometer test was carried out on a soil sample with the following results. Plot the graph and determine the Liquid Limit of the soil. $(5$ marks$)$

$\backslash$table$[[$Cone penetration $(mm),16\mathrm{.}8,18\mathrm{.}5,19\mathrm{.}9,21\mathrm{.}3,23\mathrm{.}7],[$Moisture content $(\%),21\mathrm{.}5,22\mathrm{.}4,24\mathrm{.}8,26\mathrm{.}9,29\mathrm{.}7]]$

$($b$)$ A soil sample of $250mm$ length and $125mm$ in diameter was tested in a constant head permeameter. Water seeps through the soil under a constant head of $225mm$ for $4$ minutes & $26$ seconds and the discharged water collected was $286cm3.$ Determine the coefficient of permeability, $k$ in $\frac{m}{s}.(5$ marks$)$