How is surface area to volume ratio related to cell size?
It relates to the ability of a cell to perform biochemical reactions.
A cell must be the correct size to allow the proper concentration of reactants that is needed to carry out biochemical processes. Having too great of an overall surface area (a surface area not created via things like folds, dips and cilia) is more area that must be maintained. The cell must also be small enough to allow diffusion over short distances. A larger overall surface area is like having a filled water balloon; after a certain point the limits are not increasing so much as straining. Cells usually only get as big as one square meter and often keep it much smaller.
Long story short; cells reduce the "obvious" surface area because being smaller overall helps them to perform functions. They use less obvious solutions to maximize surface area for reactions: cilia, dips, folds, and ridges.