you want to do a bouleans difference not intercection.. if you want to orient the move tool correctly, you can go to Modify>Center Pivot.. or press insert and move the tool manually..

create a new circle, and place the cylinder sphere thing so that it is lined up on the edge of the sphere.. no attaching is required.. x will allow you to move things so that it moves on the graph and is easier to line things up.. you need to hold down x while you do it.. not just press it..