Q$4.$ A falling head permeability test was performed on a cylindrical soil sample

$($diameter $=7cm,$ length $=10cm).$ The initial head at time $t=0$ was $40cm$ and during

the test it dropped by $6cm$ in $12$ minutes. The diameter of the standpipe was $0\mathrm{.}8cm.$

a$).$ Calculate the coefficient of permeability in $c\frac{m}{s}.$

b$).$ Determine the duration of the test $($in minutes$)$ for the final head to be $30cm.$