As cells become larger – otherwise holding to the same shape – their cytplasmic contents become larger relative to the area or total amount of their plasma membrane.
For all cells nutrients must cross a lipid bilayer to enter the cell. The more cell there is relative to lipid bilayer then the more material that must cross this lipid bilayer per unit area of a cell membrane. The rate of such movement becomes limiting to the metabolism of the cell if there is too much cell and not enough lipid bilayer.
As shapes become larger, their volume increases as a cube function (i.e., x3 where x is some measure of object diameter) whereas their surface area increases as a square function (that is, x2). The result is that larger objects inherently possess a smaller surface-to-volume ratio than do smaller objects. In the case of cells, this means that they possess larger volumes of cytoplasm relative to the area of their plasma membranes.
In biology there are numerous solutions to what otherwise serves as an impediment to the size of organisms. One is for a cell to change shape, such as to elongate into filaments or flatten, which has the effect of increasing surface area and/or decreasing volume. Another approach is to have nutrients predominantly cross internal rather than external membranes, that is, as via endocytotic mechanisms such as phagocytosis or pinocytosis. A yet additional and common approach is to increase in size via multicellularity rather than displaying very large individual cells.
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