This is a wrong impression. These processes fit together tightly, leaving a minimal extracellular space. The dendritic tree is the receptive part of the neuron. The axon conveys the signal to its target. The cell body contains the nucleus and most organelles that perform the synthetic and catabolic activities that keep the neuron and all its parts alive and functioning.
Neurons come in all sizes.
Motor neurons, which are the largest cells in the CNS, have a cell body measuring up to 135 microns. Granular neurons of the cerebellum, which are the smallest, measure 4 microns. The neuronal body balloons. The cytoplasm becomes smooth and the nucleus is displaced toward the periphery of the cell. This appearance, which is called central chromatolysis , is a reversible change that develops during repair of a neuron that has been disconnected from its target.