Very small animals are rarely found in polar regions.give reason?

1 Answer
Nov 4, 2017

The smaller the linear dimensions the greater the ratio of surface area to volume, and therefore the greater the heat loss (relative to size)

Explanation:

Heat loss (assuming the external temperature is greater than an animal's internal temperature) is a function of the animal's exposed surface area.

The surface area increases by the square of the linear size of the animal;
the volume only increases by the cube of the linear size.

If the volume of an animal is increased by a factor of #f (> 1# for an "increase")
then its linear dimensions are increased by a factor of #root(3)(f)=f^(1/3)#
and its surface area is increased by #f^(2/3)#

If #f > 1# then #f^(2/3) < f#

That is, increasing the volume increases the surface area (and thus the heat loss per unit of volume) by a less than 1.