I am reading Rice's book of mathematical statistics, and I have understood that if we visualize a joint probability density function (pdf) of 2 continuous random variables, then in 3D space they define a plane of course, but the pdf itself, or in other words the probability that the 2 random variables fall within a region for the joint pdf, is essentially a volume, since the pdf is defined on the third axis:

So this is a volume in 3D space.
My question is what happens in a multivariate probability density function of 3 continuous random variables. How can we visualize that? Is the probability that the 3 random variables fall within a region still a volume in 3D space? Or is it 4D space?