An uncharged, nonconducting, hollow sphere of radius 10.0 cm surrounds a 10.0-uC charge located
at the origin of a Cartesian coordinate system. A drill
with a radius of 1.00 mm is aligned along the z axis,
and a hole is drilled in the sphere. Calculate the elec-
tric flux through the hole.

Explanation:

The whole surface of hollow sphere = 4π r²

= 4 x 3.14 x (10 x 10⁻²)²

= 12.56 x 10⁻² m²

Area of the hole ( both side ) = 2 x π r²

= 2 x 3.14 x (10⁻³)²

= 6.28 x 10⁻⁶ m²

flux coming out of given charge at the centre as per Gauss's theorem

= q / ε₀ where q is charge at the centre and  ε₀ is permittivity of the medium .

= 10 x 10⁻⁶ / 8.85 x 10⁻¹²

= 1.13 x 10⁶

This flux will pass through the surface of sphere so flux passing through per unit area

= 1.13 x 10⁶ / 12.56 x 10⁻²

= 8.99 x 10⁶ weber per m²

flux through area of hole

=  8.99 x 10⁶ x 6.28 x 10⁻⁶

= 56.45 weber .

that would be b i just took the test : )