Q: How to calculate the volume of a section of a convex body? The following is essentially a partial case for my previous question.
Let $B\subset\mathbb{R}^m$ be the unit ball with respect to a concrete norm on  $\mathbb{R}^m$, say $l^p$-norm, $p\in (1,\infty)$. Let $v_1,...,v_n\in \mathbb{R}^m$ be linearly independent.

How to calculate the $n$-dimensional volume of $B\cap span\{v_1,...,v_n\}$?

I need to express this volume through the coordinates of $v_1,...,v_n$, or perhaps through some distances between certain combinations of them. I know that there is extensive literature on related matters, but I hope that this specific question has a specific answer..

A: See http://matwbn.icm.edu.pl/ksiazki/sm/sm88/sm8817.pdf and references therein to other papers by same author to see how to calculate these sections. 
