Electric field of a cylinderical insulator

[peaceandlove]

Homework Statement

A long cylindrical insulator has a uniform charge density of 1.79 µC/m and a radius of 3 cm. What is the electric field inside the insultor at a distance of (a) 2 cm? [Answer in units of N/C] (b) 10 cm.

Homework Equations

∫ E • dA = Q_enclosed / e_0

The Attempt at a Solution

I know I have to use Gauss’ Law by constructing a cylindrical Gaussian surface of radius r (r<R) and length l. However, I can't seem to figure out how to get the height to cancel out since it isn't given in the question.

 

[peaceandlove]

I figured out part a, but I'm still stuck on b.

 

[peaceandlove]

Figured out part b.