As cells grow, their surface-to-volume (S:V) ratio decreases. But don't the surface area and volume both increase when cells grow? Let's look at the mathematics...

Although cells are not perfect cubes, we can use a cube's dimensions to illustrate the concept of S:V ratio. Since all the dimensions (l = length; w = width; h = height) of a cube are the same, we can derive the following equations, where "x" represents any dimension:

These equations show that the volume of a cube increases faster than the surface area since the volume is raised to the higher exponent. For example, let's look at the surface area and volume of a small cube compared to a large cube.

As you can see, the small cube's surface area is larger than its volume, but the large cube's volume is larger than its surface area. Thus, the small cube has a large S:V ratio, and the large cube has a small S:V ratio. For this pattern to be true, the volume must grow faster than the surface area, which is why the S:V ratio decreases as a cell grows.

You might have noticed that you and I are not giant, single cells. Instead, we are made of trillions of microscopically small cells. But why? Why are small cells more efficient?

Large, voluminous cells have many moving parts. They require many structural (e.g. cytoskeleton) and functional proteins (e.g. enzymes) just to stay alive. These proteins are constantly being damaged, meaning new proteins must constantly be synthesized to replace old proteins. To meet this demand, cells also require lots of energy and resources, and must get rid of lots of metabolic waste.