Gauss's Law and a hollow metal cylinder

[flyingpig]

Homework Statement

A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of lambda, and the cylinder has a net charge per unit length of 2lambda. From this information, use Gauss's law to find (a) the charge per unit length on the inner and outer surfaces of the cylinder and (b) the electric field outside the cylinder, a distance r from the axis.

The Attempt at a Solution

My book says inside the surface, E field is 0. But I don't understand, isn't the wire a conductor spreading E fields of its own?

[PLAIN]http://img833.imageshack.us/img833/8741/98449368.jpg

 

[flyingpig]

Is inside the shell not the same as being on the surface of the shell?

 

[cupid.callin]

maybe that "inside the surface" means that inside the metal of shell (the thin layer)