In relation to surface area, how do you think a gigantic cytoplasm would affect a eukaryotic cell of a multicellular organism?
A larger cell would not be able to transport enough oxygen or nutrients into the cell, nor would it be able to move wastes or other cellular products out of the cell through the cell membrane.
The reason that cells can only get so big has to do with the relationship between surface area and volume.
Let's assume that a cell is perfectly spherical in shape with a radius of r. Its surface area (A) could be expressed as:
A = 4πr^2.
The same cell's volume (V) could be expressed as:
V = 4/3πr^3.
Let's assume that a cell has a radius of 2µ. In that case, the surface area or the total size of the cell membrane would be:
A =43.142^2 which equals 50.24 square micrometers.
The volume of that same cell would equal:
V = 1.333.142^ which equals 33.51 cubic micrometers.
Now, let's double the radius of the cell so that it's twice as large across.
Using the formulas provided above, we see that the new surface area is about 201 square micrometers, but the new volume is about 268 cubic micrometers. Therefore, when we grew the cell's radius from 2µ to 4µ, the surface area grew by a factor of four, but the volume grew by a factor of about eight.
Can you see where this is going? As a cell gets larger and larger, its volume increases at a much higher rate than its surface area. All nutrients and oxygen coming into the cell, and all cellular products and wastes leaving the cell must pass through the cell membrane. If the cell gets too big, the cell membrane will not be large enough to transport these substances into or out of the cell.