An insulating sphere of radius a carries a total charge $q$ which is uniformly distributed over the volume of the sphere.

I'm trying to find the electric field distribution both inside and outside the sphere using Gauss Law.

We know that on the closed gaussian surface with spherically symmetric charge distribution Gauss Law states:
$\frac{q}{ε\_0}= \oint \vec{E} \cdot d\vec{A}$

1. Outside of sphere:
Logically, the charge outside of a sphere will be always on the Gaussian surface and it doesn't change, therefore the electric field outside of a sphere:
$E=\frac{q}{4πε\_0r^{2}}$
2. Inside of sphere:
Because the charge is symmetrically distributed on the surface and if I image a little sphere with radius r
inside the sphere with radius r, the little sphere will have less charge on its surface.
$E=\frac{q \ r}{4πε\_0a^{3}}$

Is this explanation sufficient?

What would be the difference if I have a conducting sphere?