Electric field at points A, B, and C inside a hollow ball?

[Dell]

as seen in the diagram below, ->
http://picasaweb.google.com/devanlevin/DropBox?authkey=Gv1sRgCL_4l4PpvP_YsQE#5314956645280048530

is a solid ball with a radius of R=5cm and a charge density of $$\rho$$=-3$$\mu$$C/m³,
inside this ball, we make a hollow ball shaped space with a radius of R/3 with its centre at 2R/3 from the centre of the big ball.

what is the Electric field at point:

A-on the leftmost point of the hollow
B-on the top point of the hollow
C-at the centre of the big ball

---------------------------------------------------
how do i do this?

i think what i need to do is say that the field is equal to (the field of the original ball) + ( the field of a ball the size of the hollow, with a charge density of -$$\rho$$ )??

for C i know that the field before is 0 since it is at the centre, how do i continue from there?

 

[Dell]

what i did so far is: $$E$$=epsilon0
i took a surface at the radius of the ball and said

$$\varphi$$=$$\oint$$EdA=EA=E(4$$\pi$$R²)

$$\varphi$$=Q/$$E$$=(V$$\rho$$)/$$E$$=(0.75$$\pi$$R³/$$E$$)

E(4$$\pi$$R²)=(0.75$$\pi$$R³/$$E$$)
E=($$\rho$$R)/(3$$E$$)

now what i will do is subtract the "field" of the imaginary ball from the field of the big ball to get the total

E=E₁-E₂
E=($$\rho$$R)/(3$$E$$)-($$\rho$$R)/(9$$E$$)
and i get

E=(2$$\rho$$R)/(9$$E$$)
but where is this answer valid for? A,B or C?? is this the field at A since i took the radius of the big ball and found the flux according to that? for the others do i need to do the same using the radius 2R/3 for point B and C and saying the field of the big ball alone at C is 0?