Final answer:
RNA polymerase I is primarily responsible for the transcription of most rRNA genes in eukaryotic cells, which is critical for ribosome assembly and protein synthesis.
Step-by-step explanation:
The RNA polymerase mainly responsible for the transcription of most rRNA genes in a eukaryotic cell is RNA polymerase I. This enzyme initiates transcription at promoter sequences with the aid of initiation proteins. While RNA polymerase II transcribes all of the protein-coding genes and some snRNA genes, and RNA polymerase III transcribes some rRNA genes (like the 5S rRNA), tRNA, and other small RNA genes, it is the RNA polymerase I that is specifically tasked with synthesizing the lion's share of rRNA, which is essential for ribosome assembly and protein synthesis.