Cell efficiency

When you tutor Biology 12, one topic that comes up is cell efficiency.  It’s a bit tricky for some people, because it involves some math.

Putting it simply, imagine a cell is a sphere.  Its volume is what it needs to maintain, whereas its surface area is where it gets its supplies.  You can quickly realize that it’s best to have a big surface area compared to volume (or surface area to volume ratio), so the cell can easily get enough supplies to feed its volume.  Efficiency, in this context, refers to the cell’s surface area to volume ratio:

(1)   \begin{equation*}Eff.=\frac{SA}{V}\end{equation*}

As the radius of a cell grows, its surface area grows, but its volume grows more quickly.  Therefore, its surface area to volume ratio decreases:  its efficiency decreases.

Therefore, cells are better off being small – which is why most cannot be seen with the naked eye.  Ultimately, this same principle (of efficiency) is why a rat can run up the side of a building with ease, but a human cannot.  The human’s muscles, since they have such greater volume than the rat’s, are much less efficient.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC

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