Add a round-half spherical edge to a cylinder surface

Question

I have the following cylinder:

And I want to turn the selected area (as seen in the pic) into a half-sphere similarly to this picture. Do you have any idea how to do that?

Answer 1

Remember to turn on snap to vertexes first (ShiftTab).

1. In orthographic view, move 3D cursor to face where you will add sphere (select face of cylinder > ShiftS to set 3D cursor to selected).
2. Add UV sphere with settings of your choosing.
3. Cut sphere in half where it will join (Z key to set the viewport shading to wire-frame, CtrlB to box-select half the sphere, then delete it by pressing X to remove faces).
4. Move sphere into object (ShiftZ if you're bringing it down to align it).
5. Resize sphere with S (vertex-snap it to the edge of cylinder).
6. Remove doubles (button in tool shelf on the left) to get rid of the duplicated vertices.

Here is the process in an animated gif:

Answer 2

1. Select the area where you want to add the semisphere (the same selected vertices in your picture).
2. Move the 3D cursor to the center of the selection.
3. Move the camera so that you're looking at the area from the side.
4. Select the left-most vertex of the previously selected area.
5. Use the spin tool to generate an 90 degree arc. You should get something like this:
6. Move the camera to the top of the cylinder.
7. With the vertices of the arc selected, use the spin tool again, now rotating 360 degrees and using as many steps as the number of vertices on the face of the cylinder. The result should look like this:
8. Select everything, and use "remove doubles".