Carbon steel can be converted into martensite by heating the steel above its eutectic temperature and then rapidly quenching it. In a particular experiment, a steel pellet, \(1 \mathrm{~cm}\) in diameter at room temperature, was heated in a furnace at \(800^{\circ} \mathrm{C}\) to its eutectoid temperature and then quenched in water at \(25^{\circ} \mathrm{C}\) to a temperature of \(200^{\circ} \mathrm{C}\) in \(5.4 \mathrm{~s}\) to produce martensite. Calculate the eutectoid temperature and the time of furnace heating assuming the sphere started out at \(25^{\circ} \mathrm{C}\).

\[\begin{array}{lll}ho_{\text {steel }}=7500 \mathrm{~kg} / \mathrm{m}^{3} & C_{p \text { steel }}=500 \mathrm{~J} / \mathrm{kg} \mathrm{K} & k_{\text {steel }}=46 \mathrm{~W} / \mathrm{m} \mathrm{K} \\h_{\text {furnace }}=180 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~s} & h_{\text {water }}=1000 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~s} &\end{array}\]