Let’s see… firstly it would float around, of course. It would also tend to take the shape of a kind of sphere (a very hot sphere!).
Then, if it is in the vacuum of space, it would actually cool down slower than if it was on Earth because there is no air around it to “absorb” the heat. But even if slowly, the surface of the sphere would cool down first and solidify, forming a kind of solid layer (still very hot!) above the liquid lava below.
This is a kind of a mini-model of the Earth. We have a solid crust on the outside with liquid lava on the inside. The difference is that Earth is much bigger and much denser on the inside, so actually the Earth has a solid core below the liquid lava. Our “lava ball” would not have it.
And slowly the lava ball would continue to cool down, eventually solidifying all the way inside as well.
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