Charge distribution of a hollow conductor

Caulibeam

1. The problem statement, all variables and given/known data

We are given that there is a hollow conducting sphere with a charge 1C (to simplify things) inside it and are asked to find the charge per unit area on the inner and outer surface of the sphere. Inner radius of the sphere is 1m and outer radius is 2m

2. Relevant equations

In the answers given by another student he did this:

surface charge density inner = q/Ainner = 1/ (4pi*1^2) where A is the area
and
surface charge density outer = q/Aouter = 1/ (4pi*2^2)

3. The attempt at a solution

However in my opinion, since it is a conductor. the charge will be equally distributed within the outer and inner surface since its spherical in shape and so

surface charge density = q/(Aouter + Ainner)