$2\mathrm{.}6$ A hollow sphere $($k $=20$ W$/$m C$)$ has an inside diameter of $6$ cm and an outside diameter of $12$ cm$.$ The inner surface of the sphere is at $300$ C and the outer surface convects to the surrounding $25$ C air with a convective coefficient of $15$ W$/$m$2$ C$.($a$)$ What is the rate of heat flow through the wall of the sphere? $($b$)$ If insulation is added to the outer surface of the sphere, what thickness of insulation $($k $=0\mathrm{.}035$ W$/$m C$)$ is needed to reduce the heat flow of Part $($a$)$ by $50\%?$