Steel balls \(10 \mathrm{~mm}\) in diameter are annealed by heating to \(1150 \mathrm{~K}\) and then slowly cooling to \(450 \mathrm{~K}\) in an air environment for which \(T_{\infty}=325 \mathrm{~K}\) and \(h=25 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Assuming the properties of the steel to be \(k=40 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), \(ho=7800 \mathrm{~kg} / \mathrm{m}^{3}\), and \(c=600 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\), estimate the time required for the cooling process.