How does surface area to volume ratio limit cell size?
The surface area to volume ratio (SA:V) limits cell size because the bigger the cell gets, the less surface area it has for its size.
This is important if you are a cell that depends on diffusion through your cell wall to obtain oxygen, water, and food and get rid of carbon dioxide and waste materials.
As you get bigger, your outside is unable to keep up with needs of the inside.
We can see this with agar cubes that have been soaked in NaOH solution.
The "nutrients" have diffused all the way to the centre of the smallest cube, but the largest cube is mostly "starved" in the centre.
If you are a cell like the largest cube, your SA:V has become so small that your surface area is not large enough to supply nutrients to your insides.
At this point, you must divide into smaller cells or die.
So your size is limited by your SA:V.