As a contrast to this simple model with just a few compartments, here is a model of a Purkinje cell from the cerebellum, constructed with the GENESIS simulator by De Schutter and Bower (1994). It has 4550 compartments and 8021 active conductances ("channels"). If you look closely, you can see that it is actually composed of many cylinders.
Why would one need to construct such a detailed model? One reason is that, if we ultimately want a simple model, it is better to throw out details after proving that they aren't significant, rather than just hoping that we didn't omit something important at the outset.
Sometimes this will lead to results that you wouldn't have expected. Here is an example from a computer simulation of the Purkinje cell, where false color is being used to represent the membrane potential throughout the cell. We can use this to find the effect of applying synaptic input at various places on the cell.