$3)(15$ points$)$ A $60$ W incandescent lightbulb has a tungsten wire filament $53\mathrm{.}3$ cm long and $46\backslash (\backslash$mu $\backslash$mathrm$\{$m$\}\backslash )$ diameter. Assuming the filament has an emissivity of $0\mathrm{.}23$ and neglecting the effects of any gas inside the bulb:

a$)$ Calculate the surface area of the filament.

b$)$ Calculate the equilibrium temperature of the glowing filament. If you did not get an answer to part $($a$)$ you may use $\backslash (1\backslash$mathrm$\{$~cm$\}^\{2\}\backslash ).$

c$)$ Calculate the wavelength of peak radiated power from the filament. If you did not get an answer to part $($b$)$ you may use $2700$ K $.$ Is this wavelength in the ultraviolet, visible, or infrared part of the electromagnetic spectrum?