How has waste leaving a cell affected its surface area to volume ratio?

The important point is that the surface area to the volume ratio gets smaller as the cell gets larger and as volume increases, surface area to volume ratio decreases. The larger a cell, the less easily it can get rid of waste and it also has more trouble getting water, nutrients and gases in. That is why we do not see giant cells. Instead we see multiple cells in larger organisms.  

One way to increase surface area is to flatten the cell. That is why red blood cells are flat discs, instead of spheres. Another way is elongation. That is why many bacteria are rod shaped, and why neurons are elongated. In fact, the human body relies on the same principle to adapt to climate. Long tall and lean folks with long arms and legs live in East Africa, because such shapes increase surface area to get rid of excess body heat to avoid heat strokes. Europeans and Asians adapted to cold climates, in contrast, have shorter arms and legs and rounder torsos to minimize surface area. to conserve body heat.