I have a question about extruding boss that goes past the container that I am extruding in

I'm not sure how to word this question correctly, so I'm going to provide some pictures first off to help visualize this.

Here are some views of what I'm creating:  http://imgur.com/gallery/un9dX 

Ok so basically I am trying to create some spokes that are extruding out of the cylinder in the middle.

Here's what I tried, in picture form first: http://imgur.com/gallery/683FN

As you can see, I made a sketch of the spokes, and then extruded them to the next surface. All is fine, except for the glaring fact that the spokes are extruding out of the body, and I don't want that!! I tried cutting the extrusions out, but it just left some unsightly holes that ruin the whole design.

Please help me with this problem! I can provide anything needed to help, such as the solidworks file or pictures of the real world object.

Sorry if I missed anything that I should've included in the post, I am new here.

SolidworksParts And Features