The Cylindrical Filament in a Light Bulb Has a Diameter $3000 ^ { \circ } \mathrm { C } \text {. }$

Multiple Choice

The cylindrical filament in a light bulb has a diameter of 0.050 mm, an emissivity of 1.0 , and a temperature of $3000 ^ { \circ } \mathrm { C } \text {. }$ How long should the filament be in order to radiate 60 W of power? $( \sigma =$ $\left. 5.67 \times 10 ^ { - 8 } \mathrm {~W} / \mathrm { m } ^ { 2 } \cdot \mathrm { K } ^ { 4 } \right)$

A) 5.9 cm
B) 7.2 cm
C) 11 cm
D) 8.6 cm
E) 9.4 cm