A long string with charge per unit length λ on it passes through a cube of side a. The minimum and maximum flux through the cube will be
If the string is along the body diagonal, the flux is maximum. Diagonal has length /(/sqrt(3)a/). So total charge is /(/sqrt(3)a/lambda/)
If the string is along a side, The flux is minimum. The side has length a. So total charge is /(a/lambda/).
Now apply Gauss's Law.