A solid copper sphere with a radius of $0\mathrm{.}1$ m is initially at a uniform temperature of $20C.$ It is suddenly exposed to an environment at $200C,$ with a convective heat transfer coefficient of $50\frac{W}{m^2}K.$ Using the lumped capacitance method, estimate the time required for the sphere to reach an average temperature of $100C.$ Properties of copper: density $=8960k\frac{g}{m^3},$ specific heat $c=385\frac{J}{k}gK,$ thermal conductivity $k=400$ W$/$mK$.(6$ marks$)$

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