Calculating Electric Field of Insulating Sphere

[Cornfused]

Homework Statement

A charged paint is spread in a very thin uniform layer over the surface of a
plastic sphere of diameter 12.0 cm, giving it a charge of -35.0 mC. Find the
electric field (a) just inside the paint layer, (b) just outside the paint layer, (c)
5.00 cm outside the surface of the paint layer.

r= .06 m
q =-35e-6

Homework Equations

E= k*(q/r^2)

The Attempt at a Solution

Here is where my problem is. I'm not sure how to start it. In particular, I'm not sure what how to deal with the charged paint. Here are some questions I have that I would appreciate help with:
1-The sphere is plastic, so I treat it as an insulator. When the paint is applied and gives it the -35 mC charge, is that charge spread uniformly throughout the sphere?
2-Since the paint gave a -35 mC charge, does that mean the paint itself is +35 mC?
3-What numbers am I suppose to use for parts A and B?

Again, I feel like there is some trick with this paint thing that is eluding me and would be grateful for any direction.

 

[DiracRules]

A charged paint is spread in a very thin uniform layer over the surface of a
plastic sphere of diameter 12.0 cm, giving it a charge of -35.0 mC.

This means that the distribution of charge is uniform throughout the sphere (answer to (1) )

Find the
electric field (a) just inside the paint layer, (b) just outside the paint layer, (c)
5.00 cm outside the surface of the paint layer.

2-Since the paint gave a -35 mC charge, does that mean the paint itself is +35 mC?

No. The paint has a charge of -35mC.

Here is where my problem is. I'm not sure how to start it. In particular, I'm not sure what how to deal with the charged paint.

This problem has a precise symmetry (spherical). Usually these kind of problem are more difficult (but not impossible) to treat with the "standard" equation of coulomb E=k q1/r^2.
There is a much more useful theorem that is usually used when the symmetry is "regular" like this: the Gauss theorem.
This is the trick you were searching :D