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Find the total time elapsed for a hollow copper sphere of inner radius \( 3 \mathrm{~cm} \) outer radius \( 6 \mathrm{~cm} \), density \( \rho=9 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3} \), specific heat \( \mathrm{s}=4 \times 10^{3} \mathrm{~J} / \mathrm{kg} \mathrm{K} \) and emissivity \( \mathrm{e}=0.4 \) to cool from \( 727^{\circ} \mathrm{C} \) to \( 227^{\circ} \mathrm{C} \) when the surrounding temperature is \( 0 \mathrm{~K} \).(for inner surface \( e=1 \) Stefan's constant \( \left.\sigma=5.6 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}^{4}\right) \)
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