Estimating how many cells there are, only knowing one slide

Hello. This is my first post on the forum, I hope I'm posting in the right place.

I have a problem related with cell biology that certainly is very common in practice: estimate how many cells there are inside something only have some slide.

My problem is as follows.

Let D a cylinder of height H=5000, with circular base of radius R=500, which contains cells (spheres) of radius r = 5 floating in a liquid uniformly distributed.

We freeze D and make a slide parallel to the base of D with height h=5 (a slide like a coin of radius R=500 and height h=5). We can count the number of pieces (slides) of cells contained inside the "coin" (of course, each slide of cell inside the "coin" has different radius).

I need to estimate how many cells there are inside of D, but I also have one slide of D.

How can I estimate how many spheres there are in D? What mathematical tools can I apply?
Or maybe I need to change a bit the statement in order to have some practical solution.

Thanks in advance!