Hardening a Steel Sphere. To harden a steel sphere having a diameter of $50\mathrm{.}8mm,$ it is heated to $1033K$ and then dunked into a large water bath at $300K.$ Determine the time for the center of the sphere to reach $366\mathrm{.}5K.$ The surface coefficient can be assumed as $710\frac{W}{m^2.K},k=45\frac{W}{m.K},$ and $=0\mathrm{.}0325\frac{m^2}{h}.$