Answer
A simple answer is that the synthesis of the ribosome takes place in the nucleolus and assembly takes place in the cytoplasm, but the process of making a ribosome is more complex than that.
Work Step by Step
The truth is that both nucleolus and cytoplasm are important sites of ribosomal synthesis and assembly. The materials of the ribosome are proteins and nucleic acid. The proteins of the ribosome are made in the cytoplasm by mature functioning ribosomes and imported into the nucleolus. RNA synthesis and most of the assembly process occurs in the nucleolus on nucleolar r-RNA. The nearly complete ribosomal sub-units are exported out through the nucleolar pores into the cytoplasm where large and small subunits are put together to form the functional ribosome.
