Can someone explain what is referred by the cross sectional area of a solenoid? Is this the same for an air solenoid vs a solenoid with a solid core vs a solenoid with a hollow core?

the cross section refers to the way in which it is wound, in general to the circle

circle does not depend on what it has inside

Explanation:

A solenoid is a wire wound in general in a circular shape, even when it is not forced, the cross section refers to the way in which it is wound, in general to the circle and is joined to determine the area

          A = π r²

This circle does not depend on what it has inside, that is, it is the same section in the air, in a liquid or with a solid inside,

the entire statement is true and correct.  

there's no diagram, nothing is illustrated, and no question is asked.

see earlier