A heater has a nickel heating filament with a temperature coefficient of resistance α=0.0068 K⁻¹ and with a resistance R0=80 Ω at the room temperature T0=293 K. After turning on the heater, the filament becomes red-hot at the temperature T=1100 K thanks to a current I=2 A passing through it. What is the total surface of the filament (in m²), assuming that the filament transfers heat only by radiation (acts as a black body)?