You are casting copper into a gray cast iron mold. The part is a solid frustum with a larger diameter of $16$ mm$,$ a smaller diameter of $10$ mm$,$ and a height of $36$ mm You may assume that the gate is cylindrical with a diameter of $4$ mm$,$ has zero length, and is located in the center of the bottom of the part. The mold is maintained at $200C.$ The overall heat transfer coefficient between the completely solidified cast metal and the mold is $185\frac{W}{m^2}-C.$ The overall heat transfer coefficient between the metal being cast when any liquid metal is present in the mold and the mold is $591\frac{W}{m^2}-C.$

Determine the time from pouring to solidification if the part is poured at $120C$ above its melting point.