Sketchup's way of making a fillet

How do I make a round top on the mast?

Here is how I would do it.

  1. Start by drawing a rectangle that stands on edge vertically, which will be used to form the profile of the rounded cap to be added to the cylinder.
  2. Add an arc on the outer edge of the rectangle (a temporary guide line can help position the arc to make it an accurate quarter-circle). Delete the now-unneeded corner of the rectangle to finish the profile.
  3. Use the Follow Me tool to “lathe” the profile around the circumference of the cylinder. Select the rim (circle) on top of the cylinder, then activate the Follow Me tool. This will automatically de-select the circle, but SketchUp remembers that the circle had been selected when the tool was chosen, and will use that circle as the path for the next Follow Me action. With Follow Me active, click on the profile face. The rounded cap will form.

There will be a circular face at the former location of the top of the cylinder, which will need to be deleted (select and temporarily hide the cap, then select and delete the face).

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If you want a full half dome just use the pie tool and follow me.
Half dome

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When I click on 'the face to extrude , the face and profile disappear.

Let me guess, the model is sized to 3d print, so the end of the mast is very small.
This will make things disappear.
Scale your model up by 100 and try again.

Yes, that was it. Thank you