Ribosome synthesis takes place in the nucleolus, which is a specialized region within the nucleus of eukaryotic cells.

Here's a breakdown of the process:

* Ribosomal RNA (rRNA) genes are transcribed in the nucleolus.

* Ribosomal proteins are synthesized in the cytoplasm and transported into the nucleolus.

* rRNA and ribosomal proteins assemble into pre-ribosomal particles.

* Pre-ribosomal particles mature and are transported to the cytoplasm, where they become functional ribosomes.

So, while ribosomes carry out their function in the cytoplasm, the key steps of their synthesis occur within the nucleolus.