Well, the chapter 54: Snowball in Randall’s book What If? 2 contains the following, semi-related graphic:
(Maximum diameters of spheres of various materials before collapsing under their weight, which is about the same as the material’s free-hanging length)
This sounds like a job for https://what-if.xkcd.com/
Is there enough obsidian on this planet? Would its weight crush the earth’s crust? How would we construct it?
Constructing it is easy, just get a couple hundredthousand buckets of water and lava and bob’s your uncle
Well, the chapter 54: Snowball in Randall’s book What If? 2 contains the following, semi-related graphic:
(Maximum diameters of spheres of various materials before collapsing under their weight, which is about the same as the material’s free-hanging length)
I think the answers are yes, somewhat (in addition to collapsing under its own weight), and probably impossible.