@Joel David Hamkins Thanks for your very detailed answer. Indeed, my problem formulation on $\mathbb{R}^n$ is problematic and imprecise. Thanks for pointing it out. I'm glad to see your first two theorems are established by restricting $\mathbb{R}^n$ to a countable dense set, which is what I meant.

@Robert Israel and @Igor Rivin: Thanks for the remark. I've updated my question accordingly.

Thanks Anton Petrunin and Ilya Bogdanov for the nice answer and explanation. To complete the answer, the maximal area of the intersection of a $D$-cube with a $(D-1)$-dimensional hyper plane is $\sqrt{2}L^{D-1}$, where $L$ is the edge length of hypercube. jstor.org/stable/2046239

It takes me some time to understand the result. While searching related literatures, I found this "Integral geometry and geometric probability By Luis Antonio Santaló, pp71" books.google.com/… From my point of view, 'Remark''s answer looks like a generalised version of eq(5.10) in $\mathbb{R}^{n}$ when the breadth $a=0$.

I just realised that most published results give $\mathbb{E}|T|$ when K is infinity, whereas I'm mostly interested in a convex ploytope tessellation with small number of cells. So maybe this changes everything, what if I want to find $\mathbb{E}F$ when the number of cells $K$ is small, e.g. $K<50$. In particular, is there a way to write $\mathbb{E}F$ as a function (or approximated function) of $n$, dimension of space and $K$, the number of cells?

Thanks for your information. I also found [this document] (algo.inria.fr/csolve/vi.pdf) which summaries useful statistics for Poisson-Voronoi Tessellations on $R^1$, $R^2$ and $R^3$. I haven't found any result about $(n-1)$-dimensional measure of the facets of the tessellation. Nevertheless, there are bunch of software can give asymptotic statistics by simulation, e.g. Qhull

Thanks for a very detailed answer. As the problem now becomes finding $E|T|$, I'm searching some literatures about the general result on a convex polytopes tessellation. Thanks for your help again. Furthermore, as you mentioned it in the end, I'd like to know more about restricting $L$ to axis-aligned lines.