Light transport theory - can't visualize basics

Question

I don't understand why the following should hold in light transport theory:

let p(x) be the number of particles per unit volume at the point x, then the total number of particles P(x) in a small differential volume dV is

$$P(x)=p(x)dV$$

How come?

I don't understand: is the "small differential volume" even smaller than the unit volume where p(x) particles are counted? I can't visualize this thing geometricaly or physically

Answer 1

Think of $p(x)$ as a density: at point $x$ there are $p(x)$ particles per cubic meter, say. Then for a small volume, say $dV=$ 1 cubic millimeter, how many particles are in that small volume?