The question is much simpler than you imagine.
For a)
If the current in the circuit is given as 0.4A use the formula provided
0.4 = 0.2V³ to find V the pd across the rod
Subtract this from 6V to find the pd across the resistor. (The battery has negligible internal resistance)
You now know the pd across, and current through the resistor.
V=IR will find its resistance.