A cast product of a particular material has dimensions $75\: \text{mm} \times 125\: \text{mm} \times 20 \:\text{mm}$. The total solidification time for the cast product is found to be $2.0$ minutes as calculated using Chvorinov's rule having the index, $n =2$. If under the identical casting conditions, the cast product shape is changed to a cylinder having diameter = $\text{50 mm}$ and height = $\text{50 mm}$, the total solidification time will be ______ minutes ($\textit{round off to two decimal places}$).
