How does a cells surface area to volume ratio limit its size?

This is also the main reason that the common science fiction trope of "enlarged species" (such as wasps, ants, or spiders) is untrue: as we know from elementary geometry and physics, mass increases as volume, or a cube of the central radius, but area only increases as a square.

Therefore, at some point, the cell would burst and die because the strength of the cell wall to support the internal fluids and organisms would no longer be able to contain them. Since cell sizes range over a very wide range (0.1nm to 3m!), a final "limit" may not yet be known.

The following link provides a comprehensive list of single cell sizes broken down by type: https://tutor.hix.ai

What restricts the size of cells? Prokaryotes have large sizes because of their efficient metabolism; eukaryotic animal cells have large sizes because of a variety of factors, some of which are unknown; and plant cells have large sizes because of their large central vacuoles, which fuel their growth.

The surface area to volume ratio of a cell determines its maximum size because as a cell gets bigger, its volume grows faster than its surface area. This means that the cell has less surface area in relation to its volume, which affects how well it can exchange materials with its environment through processes like diffusion. If a cell gets too big, it might find it difficult to move waste products, nutrients, and oxygen, which could cause problems with cell function and possibly even lead to cell death.