P $2$ A cylindrical riser must be designed for a sand$-$casting mold. The casting itself is a steel

rectangular plate with dimensions $7\mathrm{.}5cm12\mathrm{.}5cm2\mathrm{.}0cm.$ Previous observations have indicated

that the total solidification time $($TTS$)$ for this casting $=1\mathrm{.}6$min. The cylinder for the riser will

have a diameter$-$to$-$height ratio $=1\mathrm{.}0.$ Determine the dimensions of the riser so that its TTS $=2\mathrm{.}0$

min.