Charge density in cylinder with uniform charge

[p0ps1c1e]

1. A charge density ρ (charge per unit volume) is distributed uniformly throughout a non-conducting cylinder of radius R. What is the magnitude of the electric field a distance r = R/2 from the cylinder's axis?

Homework Equations

E ∫dA = q(interior)/ε₀[/B]3.

So I tried doing EA = (ρA)(v/V)/ε₀ where v is the volume of the Gaussian surface and V is the volume of the cylinder

E = (ρ*(πR^2L/4πR^2L))/ε₀
E = ρ/4ε₀

However the answer is supposed to be E = ρR/4ε₀

I'm not sure where I'm going wrong

 

[BvU]

Check Gauss law once more: one is a volume (to determine q(interior) ) and the other is an area (of the surface).