How does the eukaryotic cell overcome the problem that is inherent from evolving to be larger

the cells 'evolved' to be smaller and smaller and smaller, increasing the surface area to volume ratio
This is good because the cell has a lot of surface area to take in food/nutrients compared to the volume it took up

The larger an object is, the smaller the surface area to volume ratio. One way to increase surface area while keeping the volume constant is to lengthen an object. Another way is to flatten it. A cylinder has more surface are than a sphere of the same volume. That is why we see many cylindrical cells in nature. Pancakes have even more surface areas than cylinders. That is why the red blood cells are flattened disks, to maximize the surface area they have.

most cell biologists would agree that the issue for a growing cell is its ability to generate energy across membranes, such as with oxidative phosphorylation. the internalization of mitochondria, who were once independent, small bacteria-like cells, enabled the massive eukaryotic cells to sustain their size with energy production across the mitochondrial membranes that were now inside their own plasma membranes.