Earlier quoted context omitted.
Why?
Humans are notoriously terrible about estimating volumes when things are curved and volume functions are exponential. A great example of this done in 8th grade science classes across the US is to put 100ml of water in a 100ml graduated cylinder, 150ml in a 1L beaker, and ask the class which has more. Humans are awful at estimating how much volume the increased radius adds, and usually will say the 100ml. The problem…
(Fair point that people are lousy at estimating even polynomial functions, though...)