Diameter of wire from voltage, length, resistivity

[Linus Pauling]

1. A standard 100 W (120 V) lightbulb contains a 8.50 cm-long tungsten filament. The high-temperature resistivity of tungsten is 9.0*10^{ - 7} ohm*m. What is the diameter of the filament?



2. p= resistivity, E = V/L, I = AV/pL, R = pL/A...



3. I know that I'm going to solve for A = pi*r², find r and multiply by 2 to get the diameter, but I just don't see how to do it with what I'm given. For example, I could do pi*r² = IpL/V but I don't know I, or A = pL/R but I don't know R...

 

[Stonebridge]

The information that the bulb operates at 100W and 120V allows you to calculate the current through it and its resistance. Do you know a formula relating power to voltage and current?