Final answer:
The nucleolus is the specific nonmembranous body within the nucleus in charge of rRNA formation, ribosome assembly, and directing protein synthesis in the cytoplasm after the ribosomal subunits are exported.
Step-by-step explanation:
The nonmembranous body within the nucleus that is responsible for the site of rRNA formation is called the nucleolus. The nucleolus is essential for the assembly of ribosomes, which are organelles made of protein and ribosomal RNA (rRNA), and are integral for protein synthesis within the cytoplasm. The rRNA provides a mechanism for decoding genetic messages from mRNA into amino acids. The nucleolus coordinates the synthesis of rRNA with proteins to form the large and small subunits of ribosomes. Afterward, these ribosomal subunits are transported out to the cytoplasm where they direct protein synthesis.
Various types of rRNA, such as 5S, 5.8S, 18S, and 28S in eukaryotes, are synthesized by RNA polymerase I within the nucleolus. These rRNAs, in association with ribosomal proteins, assemble and undergo processing before the ribosomal subunits exit the nucleus into the cytoplasm. There, they associate with mRNAs on ribosomes to translate new proteins.
Additionally, many ribosomes are found associated with the rough endoplasmic reticulum (ER), playing a crucial role in the synthesis of proteins that are destined for the Golgi apparatus.