I will use one time again the magical function Line-Line (with no scale or other if needing) ;)

With 4 clicks + Helper Lines you can have any positions / Rotations! ;)
and not headaches of the Orient function, CPlane etc... ! :)

If you want insert your cylinder inside the sphere
...the more easy is draw a "Point" on the axe of the cylinder at distance from the base needing
So you can take this point as "markers" for your Line-Line function.
This can be made also by the Helper Lines themselve (Relocate) but..."Point" is more visual! :)