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There is a direct relationship that exists between surface area and heat loss in organisms. The larger the surface area, the greater the heat loss from the organism, and vice-versa. Whether you believe in evolution or not, this reason actually makes sense. Organisms that exist in extremely cold environments, such as the north pole-south pole extremes, have smaller surface area to volume ratios. This helps them conserve body heat. It is also interesting to note there are few, if any, ectothermic organisms living in this type of environment. Ectotherms are organisms like reptiles which rely on outside sources of heat to warm and stimulate their internal temperature. 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. Their body limbs are much larger and thinner, to help radiate excess body heat into their surroundings.
This can be demonstrated using any number of geometric objects. Consider two cubes, one with an edge length 1 m and a second one with an edge length of 2 m. The surface area of the first cube is 6 m² and the volume is 1 m³. The surface are of the second cube is 24 m² and the volume is 8 m³. Observe that the surface area increased by the square of the dimension change and the volume increased by the cube of the dimension change. This is a general characteristic.
The rate of heat loss can be shown to be related to the surface area to volume ratio. As animals get larger, the ratio of their surface area to volume reduces. This means they retain heat better (i.e. they lose heat at a lower rate).
This is often used as the reason why a shrew must be a very aggressive little animal because it must eat to compensate for its high heat loss rate. An elephant does not need to eat as much relative to its weight because its heat loss per pound is less.
The larger the surface area, the faster the heat loss, because then there would be more area for the heat to come from. Like compare a thin sheet of ice to an ice cube of the same mass, which would melt first? The sheet, because it has a larger surface area.
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