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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.

enter image description here

enter image description here

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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. UVsphere

Now, in edit mode, Select the Top half Vertices of the Sphere. Top Vertices Selected Delete Them. After Vertices are Deleted 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. Extruded & Scaled UV Sphere Now, press Ctrl+Tab and Select "FACE" selection mode. Select the 2 faces on X axis. Face Selected on X-Axis Now, Simply press E to extrude and the G to move & X to constrain the movement on X axis. Move it out ward. then Press S & X & 0 to even out the extrusion. Catapult Handle And , Here is a link to file Blend File

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Choose the end vertice on the handle and the vertice on the sphere you want to connect the handle to. Now merge them with Alt+M → At last (if you chose the sphere vertice last). Do the same thing on the other side. enter image description here

You should get this. Now choose the merged vertices and subdivide (W → Subdivide). Merge the new vertice with the one on the sphere as before

enter image description here

You'll get a 5-edged face as the handle so I recommend connecting the middle vertice on the sphere to the far vertices of the handle so you get 3 triangles. You connect vertices on a face with J.

I'm sorry that I can't use more images - I don't have enough reputation to post more than 2.

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Another way for the sake of information, and admittedly, not the best way.

In edit mode, select the top ring of your catapult cup. Upper ring hit SHIFT + D, right click so it stays in the same position. After that keep the newly create mesh and hit P and select "Selection" and then exit edit mode and select your cup and hide it, then select the newly created circle and move it up, just a little.

After that select the circle, shift select the plane that hold the cup, and then go to top view, then orthographic, and then select Knife Project on the left of the menu and tick "Cut through"

Quick demonstration video:

The process

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