$(30$ points$)$ A well $0\mathrm{.}5$ m in diameter penetrates $33$ m below the static water table. After a long period of pumping at a rate of $80\frac{m^3}{h}r,$ the drawdowns in wells $18$ m and $45$ m from the pumped well were found to be $1\mathrm{.}8$ m and $1\mathrm{.}1$ m respectively.

$($a$)(10$ points$)$ What is the transmissivity of the aquifer?

$($b$)(10$ points$)$ What is the approximate drawdown in the pumped well?

$($c$)(10$ points$)$ Determine the radius of influence of the pumping well.