Question

surface area - to - volume ratio is an important concept as it determines the ability of a cell to exchange materials with the environment. it is important that you be able to both calculate this ratio and also understand its significance.

1. why are cells so small? explain the relationship of surface area to volume.

a. as the size of a cell increases, what happens to the surface area to volume ratio?
b. how would this affect traffic into and out of the cell?

Explanation:

a. The surface - area to volume ratio decreases. As the cell size (radius for a spherical - like cell) increases, the volume (proportional to $r^{3}$) increases faster than the surface area (proportional to $r^{2}$). For example, if the radius of a cell doubles, the surface area becomes 4 times larger ($A = 4\pi r^{2}$, new $A'=4\pi(2r)^{2}=4A$) while the volume becomes 8 times larger ($V=\frac{4}{3}\pi r^{3}$, new $V'=\frac{4}{3}\pi(2r)^{3}=8V$). So the ratio $\frac{A}{V}$ decreases.
b. A lower surface - area to volume ratio means less surface area is available relative to the volume. Since the cell membrane is the site of material exchange (traffic into and out of the cell), a decreased ratio limits the cell's ability to exchange materials efficiently. There is not enough surface area to support the metabolic needs of the larger volume of the cell, which can lead to problems in getting nutrients in and waste out.

Answer:

a. The surface - area to volume ratio decreases.
b. It limits the cell's ability to exchange materials efficiently as there is not enough surface area relative to the volume to support metabolic needs.