$[20$pt$]$ A $200$ mm $-$diameter electric hot plate of a cookstove is located in a room whose walls and air are at $27C.$

The top surface of the hot plate is maintained at $500C.$ The convection heat transfer coefficient between the hot

plate and the air is $10\frac{W}{m^2}K,$ and the emissivity of the hot plate surface is $0\mathrm{.}9.$

a$.[10$pt$]$ Calculate the rates of heat transfer by convection and radiation, respectively.

b$.[10$pt$]$ If the electricity cost is $C_{\text{e}\text{l}\text{e}\text{c}}=$$$\frac{0\mathrm{.}15}{k}Wh,$ determine the annual cost of electricity for operating

the cookstove for $3$ hours a day.