Question

A cubical Gaussian surface encloses a charge of 8.85  1010 C in vacuum at the
centre. Calculate the electric flux passing through one of its faces.

Answer 1

The six faces of the cube are symmetrically placed around the center O of the cube.  Let the corners be A,B,C,D, E, F, G and H..  ABCD is one face. Let a sphere be drawn with radius = OA.
 
  Then 1/6th of flux around the center passes through the face ABCD. 

Using Gauss law,    integral E . dS   = q /ε

  So answer:   1/6 * 8.85 * 10^-10 / ε   units