I was teaching area and volume scale factors today and decided to finish by introducing a problem the class will attempt next lesson. As you may already know, insects respire through their exoskeleton which means that they require a volume to surface area ratio which is optimal to absorb the correct amount of oxygen. If an ant was to suddenly grow to a height, let’s say, just bigger than a human (2 metres), would it’s volume to surface area ratio be able to support the amount of oxygen it requires to respire?
I was going to give a comprehensive way of looking at this problem. However, after doing a quick search I found that someone got there ahead of me. See Jason Dyer’s blog for the worked solution.