As an engineer for a heating and cooling company you must design the refrigeration for a new ice-skating rink. As a first crack you assume a rink \(35 \mathrm{~m}\) in diameter covered by a dome \(45 \mathrm{~m}\) in diameter. The rink is kept at a temperature of \(0^{\circ} \mathrm{C}\) while the dome is at \(15^{\circ} \mathrm{C}\). If both behave as blackbody radiators, what is the net heat transfer between the dome and rink and the amount of refrigeration required?