$(25)$ The sketch shows a cylindrical container of diameter $5$ m and height $3$ m $.$

$($a$)(5)$ If the container is initially empty and the nozzle at the bottom is closed, calculate the time $($in hours$)$ needed to fill it with water if the filling rate is $Q=10\frac{m^3}{h}r(hr=$ hour$).$

$($b$)(10)$ Once the container is full, the nozzle is opened. What is the velocity $($in meters per second$)$ of the resulting free jet assuming the fluid is inviscid? $($no derivation is required$)$

$($c$)(10)$ What should be the diameter of the nozzle $($in centimeters$)$ needed to prevent overflowing?