Question

know the mathematical relationship between surface area and volume, and explain how surface to area volume affects heat loss. Which can be smaller endotherms or ectotherms  

Answer 1

There is a direct relationship that exists between surface area and heat loss in organisms. As per this relationship, larger the surface area, larger is the heat loss.

Organisms that exist in extremely cold environments like north pole-south pole extremes, have smaller surface area to volume ratios. This helps them conserve body heat. On the other hand, organisms that live in tropical, equatorial zones have larger surace area to volume ratios, which means they have a need to have a mechanism to help disperse body heat.

Endotherms -  These type use internally generated heat to maintain body temperature. Their body temperature tends to stay steady regardless of environment. Humans,  polar bears, penguins are endotherms

Ectotherms - These type mainly depend on external heat sources, and their body temperature changes with the temperature of the environment.  rattlesnakes, fishes, amphibians are ectotherms.

So out of these, mainly ectotherms have lower surface area, so heat loss will be less.