Cutting out a part of a plane from sphere vertices I'm slowly trying to learn blender. I have a mini project I want to create and 3d print a catapult (just the 'ladle' part) that I could mount to a servo motor. 

I would like to get rid of the part that is covering the half sphere and then connect the half sphere with the handle. 

There are no vertices where the sphere and handle meet so I do not really know how to deal with it.
Here are some steps for you. (Since you'll will surely make your catapult like a solid object)

First create a Uvsphere with default options.


Now, in edit mode, Select the Top half Vertices of the Sphere.

Delete Them.

press Ctrl+A to select all the vertices , Then Press E to Extrude and immediately press ALT+S to Scale the Uvsphere. Scale it outward to get a shape like this.

Now, press Ctrl+Tab and Select "FACE" selection mode. Select the 2 faces on X axis.

Now, Simply press E to extrude and the G to move &amp; X to constrain the movement on X axis. Move it out ward. then Press S &amp; X &amp; 0 to even out the extrusion.

And , Here is a link to file 
Blend File