Nose cone: Aerodynamics, as many others have touched on. You’ll see that the actual satellites are almost never cone-shaped (unless they’re designed to come back down), and also the cone is usually ditched as soon as we’re out of the atmosphere.
Cylinder: Mostly manufacturing. Rolling metal into a circle is cheap and easy, only needs a single weld (=weak point), and a circle shape can also hold the most pressure for the least material. OFC a sphere would even be better, but you can’t mount something on top of a sphere that easily.
“more stable”: Another shape would give you no real advantage, if not even a disadvantage. On the launch pad, the rocket is held in place by clamps, so you don’t really care about how intrinsically stable it is. Unless there’s a hurricane it won’t tip over. In flight, aerodynamics is everything, and here again, corners = bad. And on landing, you have legs, which again make the shape of the rocket irrelevant.
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