[Terry Capps]

In the first attached image, I have created a big tapered cylinder of revolution from a line and a smaller solid cylinder puncturing the big tapered cylinder. I SELECTED the larger cylinder, then added* the smaller cylinder to the SELECTION, and then clicked on Object, Boolean, "Knife and Cut Away" to produce the second attached image. This second image shows the big tapered cylinder with a small circular section of one side SELECTED. I then deleted that selection to produce the third image.

If you haven't read the manual, I suggest that you do. Boolean operations aren't really intuitive. The steps to perform a Boolean operation have to be done a certain way and in the correct order.

* With the first object already SELECTED, hold down the shift-key and then click on the second object.

Hints and Tips:
For most** of the Boolean operations, all objects should be 3D and have no open edges (the objects should appear to be solid). All surface NORMALS should be facing outwards. If a surface NORMAL is not visible or appears as a magenta dot, it is facing the wrong way. Select the surface (or surfaces) and then click on Surface, Flip Normal.

** The exception is when dealing with the Boolean-Knife operations. The object to be modified can be 2D, but the modifier object must be a 3D solid object. If you need to use a 2D object as a knife, try using the Knife tool under the Tools menu.