What is the fourth dimensional equivalent of volume?

[BillTre]

2D has areas.
3D has volumes.
what are 4D spaces called?

 

[renormalize]

2D has areas.
3D has volumes.
what are 4D spaces called?

Hypervolume, which is bounded by 3D hypersurfaces.

 

[DaveC426913]

Hypervolume is the only thing I've found so far.

 

[DaveC426913]

Hypervolume, which is bounded by 3D hypersurfaces.

Does 3D hypersurface track?

Do 2D denizens say "A 3D space is called a volume which is bounded by 2D hyper lines"?

Yeah, I guess it does:

"A 2D hypersurface is a mathematical term for what is typically called an ordinary surface in three-dimensional space. More generally, in mathematics, a hypersurface is an object (a manifold or variety) that has a dimension exactly one less than the dimension of the space it is embedded in."

 

[Baluncore]

A 4D sphere is a hypersphere.
https://en.wikipedia.org/wiki/3-sphere#Properties

 

[DaveC426913]

A 4D sphere is a hypersphere.
https://en.wikipedia.org/wiki/3-sphere#Properties

Yes, and hypercubes, hypertetrahedra.

Tesseract is my trigger word, so I think it's about time enough that I mention (as I do every few years) that I came very close to building my own (3D shadow of) a fully-articulated hypercube.

I solved all the enginering problems with 3D prototyping and was just gearing up to print the final parts when I discovered that someone had beaten me to it.

So that's about two decades of spare time I'll never get back.