Surface Area-to-Volume Ratio
by Greg Crowther
Written for Biology 220 at the University of Washington, this song explains the relationship between body size and mass-specific metabolic rate. It references the formulas for the surface area and volume of a cube with sides of length L: 6L2 and L3, respectively. These formulas should be written out explicitly to avoid confusion. Also, the alliteration of “large” and “low” in the line “If you’re large, it’s low” reminds students to group these two adjectives together (a large body size implies a low surface area-to-volume ratio).
Surface area to volume ratio:
If you're small, it's high;
If you're large, it's low.
Animals aren’t cube-shaped, but let’s pretend.
Say L is the length of a side -- what then?
6L to the 2 over L to the 3 equals SA over V.
SA over V.
Animals’ internal metabolic activities can’t
Exceed what they exchange with the environment.
And so, as they get wide and tall,
Their metabolic rates must fall.
Metabolic rates must fall.
• MP3 (demo)
• music video
• sheet music (with melody play-back)
Songs like this one can be used during class meetings and/or in homework assignments. Either way, the song will be most impactful if students DO something with it, as opposed to just listening.
An initial, simple follow-up activity could be to answer the study questions below. A more extensive interaction with the song might entail (A) learning to sing it, using an audio file and/or sheet music as a guide, and/or (B) illustrating it with pictures, bodily poses, and/or bodily movements. The latter activity could begin with students identifying the most important or most challenging content of the song, and deciding how to illustrate that particular content.
(1) In general, what units should surface area have? What units should volume have?
(2) What is the SA/V ratio of the hypothetical cube-shaped animal in the song? Reduce this ratio to its simplest possible form.
(3) If we were to assume that an animal were spherical, rather than cube-shaped, would SA/V be similarly affected by body size?
(4) What are some things whose exchange with the environment may be limited by the SA/V ratio?
(5) The second verse refers to metabolic rates. Which would you expect to have a higher metabolic rate: a mouse, or an elephant?
(6) Considering the specific content covered by this song, is there anything important that is missing, unclear, or misleading? If so, what?
(Answers may be found on the answers page.)