If an elephant grew to be twice its height, the area of its ears would grow by a factor of........?

Question

What factor would it grow by? ex. 2, 4

Answer 1

Hi Stella Y.,

There's a mathematical solution to this, and a separate biological solution!

Mathematically, if the elephant grows x 2 linearly, all areas grow as x 2^2, and all volumes grow as x 2^3. So the mathematical answer would be x 4. BUT, biologically, the elephant uses its ears for cooling, as its skin is other places too thick to shed heat. Since if amount of heat to be shed, proportional to elephant volume, goes up as the cube of the linear size, the ears would have to grow in area by x 8, or linearly by 8^0.5 (~2.8) factor. Or, the adult elephant would have to move more slowly, so as to generate heat more slowly. I can't detect a 1.4 factor increase (2.8/2) in proportional ear size as elephants grow from babies to adults, so I suspect the latter obtains.

If you find out otherwise, I'm all ears!

--- Cheers, --- Mr. d.