Select solid elements within enclosed volume?

Hi,
Is there a way of selecting elements within a volume (enclosed surface)?
So in my case, I have this solid hex mesh made with shrinkwrap:
<?xml version="1.0" encoding="UTF-8"?>
I now want to group the elements in separate components. For example, I want to select the elements within this tube and group them separately:
<?xml version="1.0" encoding="UTF-8"?>
I have hundreds of these enclosed surfaces that I would like to associate with elements. Doing this manually is, as you can imagine, very mundane work.
Do you have any appropriate method for this type of entity selection?

That does not really answer the question. I am trying to select the elements and move them to new comp directly.
But there is quite a lot of elements and the boundary volumes are asymmetrical and have very complex geometries.
The question I have is how to select the elements within the boundary.
Select your elements and move them to new comp directly. Why you need 'associate' to surfaces?