Yep, you’d turn it on a lathe. Even for a decent turner, it’s a tough job to get a good sphere.
You’d start by roughing the stock out to a cylinder the desired diameter of the sphere. It’s better to hold the stock in a chuck than to use a spur and live center, so that you have free access to the end. Face off the free end of the stock to square it.
Then measure back from the end of the stock and mark with a pencil where the equator of the sphere will fall. Use a skew to round off the end (it helps to have a diameter gauge to check your accuracy as you get close). Don’t turn away your equator mark; you’ll need it for the next step.
Measure again from the equator mark back toward the chuck, again the radius of the sphere. This is where the sphere will end. Mark it with a pencil. Use a parting tool to cut through about half the thickness of the stock exactly on that mark.
Now cut back some of the waste stock between the sphere and the chuck to give yourself some tool clearance. Take it all the way down to the bottom of the parting tool cut. Now comes the hard part: use the skew to begin rounding this hemisphere. Do as much as you can without cutting into the remaining connection between the sphere and the waste stock.
When you’re happy with what you have so far, and it checks out against your gauge, do most of your sanding at this point, while it’s still well supported. Then you’ll begin making alternating cuts with the skew, carrying down the curve on the sphere side and cutting away at an angle on the waste side. Eventually, the sphere will be connected by just a tiny neck of wood to the waste stock. Do a little gentle sanding on your recent cuts, and separate the sphere from the waste. Now you just have to trim away the “belly button”, sand and finish.
It’s a fun exercise to challenge your skills, but you really don’t want to have to make a lot of these!