How does the size of a cell's surface area change compared to its volume when the cell grows?

I learned this before I just don't remember

Surface area does not increase after certain growth with the same pace as the volume increases.

Explanation:

The volume of cell increases rapidly as compared to its surface area when the cell grow in size and this is the reason due to which which its surface area to volume ration gets smaller leads to reduction in surface diffusion. After a certain growth, the surface area does not increase as the material that forms the surface of the cell cannot increase further. Therefore at this stage the cell must divide and produce smaller cells which are able to accommodate favorable surface area/volume ratios