A falling$-$head permeability test was made on a sample of clayey sand whose diameter was $2\mathrm{.}5-$inches and whose length was $5-$inches. The cross$-$sectional area of the inside of the burette was $0\mathrm{.}85c{m}^2.$ After a steady flow was established, the head on the sample decreased from $105$ cm to $70$ cm over $2$ hours and $22$ minutes. Calculate the coefficient of permeability in cm$/$s$.(20$ points$)(1$ in $=2\mathrm{.}54cm)$