A solid part $($see figure$)$ of polymer material is to be fabricated by additive manufacturing $($AM$)$ in square$-$shaped layers starting from the bottom of the part working upwards. The nozzle diameter of the $($AM$)$ machine is $\frac{a}{10}mm$ and the nozzle follows a linear serpentine path parallel to the sides of the square layers with a feed rate of a$/5$ mm$/$min$.$

Ignore any tool path motions other than those involved in adding material, and any other delays between layers or the serpentine scan lines.

The time taken to fabricate this part is $q,$ minutes.