I am currently working on a project that shows the different layers of the earth, and I am using Maya to do the modeling (and animating). I started with a sphere for the core, and then built more spheres on that. Now I have the earth with the various layers, except it's the whole earth which just shows the crust. I am wondering if there is some way to cut this sphere set in half in order to show the various layers of the earth.
Your default Extrude settings are probably just too high. It looks to me like the faces are being extruded more than the radius of the sphere, so that the new faces are flipping inside out. You should be able to tweak this in the extrude command's options box, or in the history node created when you perform the operation.
Two important questions are: will you need to animate this cross-section or not? And, do you need the different layers to be cut at different angles, to show slight offsets between them?
If 'yes' to the first, you might need to look into animated Booleans or something.
If 'no' to the second, then you don't need multiple spheres--just a single one with a radial texture ramp showing the different layers.
You have to add a face to the cut sides of each layer. The spheres are hollow so when you cut them in half it won't look the way you are picturing it to. After you cut it in half select the sphere and choose mesh- fill hole. Do this for each sphere and then move each of the inner spheres slightly forward.