What Is the Electric Field at Various Distances From a Charged Spherical Shell?

[22steve]

Homework Statement

The figure below shows a spherical shell with uniform volume charge density ρ = 1.63 nC/m3, inner radius a = 6.0 cm, and outer radius b = 2.70a. What is the magnitude of the electric field at the following radial distances:
r=1.5, r=b, r=3b

Homework Equations

Q= sigma dV
flux = E x A
flux = charge enclosed/permittivity constant (8.85e-12)
k x q/r^2 = E (electric field outside a spherical shell of charge)

E = k x r(q/R^3) R= radius r= distance from center of shell to point where E is measured.

The Attempt at a Solution

I've tried integrating, and substituting different values of q into the Electric Field equations. I've gotten 18094, 82, and 1813 as answers. I would show my integration techniques, but it's kinda hard to do on the keyboard. haha

 

[rootX]

Part I:
When r = 1.5, what's charge inside the sphere of r = 1.5 m?

When r = b or r =3b, that sphere encloses all the charge. So, Q is same but Area changes for part II and part III