A paper coffee cup has a radius $=0\mathrm{.}040$ m$.$ It holds $0\mathrm{.}100$ kg of coffee $($mostly water$).$ The initial temperature of the coffee is $100\backslash$deg C$.$ Room temperature is $20\backslash$deg C$.$ Use an emissivity of $1\mathrm{.}0.$

A$)$ What is the rate of heat loss through radiation from the top surface of the coffee? 

B$)$ How much heat is lost in $10\mathrm{.}0$ min? 

C$)$ What is the temperature of the coffee after $10\mathrm{.}0$ min?