there is a lot of activity occurring inside the one hundred trillion cells within our bodies. where does most of the metabolic activity occur within the cell

Most of the metabolic activities occur in the cytoplasm of the cell.

Cytoplasm is a gel-like fluid present within the cell. It consists of all the contents enclosed within a cell membrane excluding the nucleus.

It is mainly composed of water but also contains salts, enzymes, organelles, and organic molecules.

It is the main site for most of the cellular processes such as glycolysis (first stage of cellular respiration), protein synthesis, mitosis and meiosis etc.