An engineering student has been given the assignment of designing a hydraulic holding system for a hay$-$baling system. The system has four cylinders with $120-mm-$diameter pistons with a stroke of $0\mathrm{.}320$ m $.$ The lines connecting the system are $1$ cm id $($inside diameter$).$ There are $15\mathrm{.}5$ m of lines in the system. For proper design, the reserve tank should hold a minimum of $50\%$ more than the amount of hydraulic fluid in the system. If the diameter of the reserve tank is $30\mathrm{.}49$ cm $,$ what is the shortest height it should be$?($Round the final answer to four decimal places.$)$

The shortest height that the tank should be in $$ cm $.$