I think C\propto R is applicable for any other curved geometrical shape(R=radius of curvature);so, you can assume any shape.
You are right, one can prove it for any curved conductor but the problem arises when we are dealing with cubical(or such other shapes) conductors, as radius of curvature...
[b][FONT="Arial Black"]1.Prove that free charge resides on the surface of a conductor.(Using Gauss's law or laws of capacitance) Homework Equations
The Attempt at a Solution
I could not figure out how to prove this using Gauss's law,though i tried to solve it using the laws of capacitance.This...