$1-9$ A solid copper sphere $(k=350\frac{W}{m}C$ has a diameter of $10$ cm and is resting on a

tabletop. An internal heater keeps the surface of the sphere at $200$ C $.$ The surface of the

sphere is highly polished and has an emissivity of $0\mathrm{.}08.$ The convective coefficient is $12\frac{W}{m}2$

C$.$ The room air is at $20$ C and the surroundings are at $18$ C $.$ Assume the heat flow from the

sphere to the table by conduction is negligible.

$($a$)$ What is the heat transfer rate by convection $($W$)?$

$($b$)$ What is the heat transfer rate by radiation $($W$)?$