In Betty Crocker's Cookbook, it is stated that it takes 2 h 45 min to roast a $3.2-\mathrm{kg}$ rib initially at $4.5^{\circ} \mathrm{C}$ "rare" in an oven maintained at $163^{\circ} \mathrm{C}$. It is recommended that a meat thermometer be used to monitor the cooking, and the rib is considered rare done when the thermometer inserted into the center of the thickest part of the meat registers $60^{\circ} \mathrm{C}$. The rib can be treated as a homogeneous spherical object with the properties $\rho=1200 \mathrm{~kg} / \mathrm{m}^3, c_p=4.1 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}, k=0.45 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$, and $\alpha=0.91 \times 10^{-7} \mathrm{~m}^2 / \mathrm{s}$. Determine (a) the heat transfer coefficient at the surface of the rib; (b) the temperature of the outer surface of the rib when it is done; and (c) the amount of heat transferred to the rib. (d) Using the values obtained, predict how long it will take to roast this rib to "medium" level, which occurs when the innermost temperature of the rib reaches $71^{\circ} \mathrm{C}$. Compare your result to the listed value of 3 h 20 min .
If the roast rib is to be set on the counter for about 15 min before it is sliced, it is recommended that the rib be taken out of the oven when the thermometer registers about $4^{\circ} \mathrm{C}$ below the indicated value because the rib will continue cooking even after it is taken out of the oven. Do you agree with this recommendation?