Problem $3(15$ pts $)$

A $3-$meter$-$high room with a base area of $4m4m$ is to be heated by electric resistance heaters placed on the ceiling, which is maintained at a uniform temperature of $35C$ at all times and has an emissivity of $0\mathrm{.}9.$ The floor of the room is at $20C$ and has an emissivity of $0\mathrm{.}8.$ The side surfaces are well insulated. Determine the rate of heat loss from the room through the floor.