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6. Size-related properties
Several important properties of objects are determined by their size. Consider a mother seal and her pup living on the sea ice in Antarctica. The animals are homoiothermic ('warm-blooded') and they maintain their internal temperature by excess heat production by body tissue. Since the total heat production is a function of body mass, it will be related to volume, that is to the cube of body size (eg length). Heat loss, on the other hand, occurs through the surface, so is related to surface area or the square of body size. So if all other properties of mother and pup are the same, the balance between heat production and heat loss will be determined by the ratio between surface area and body volume. So if the mother is twice the size of the pup, we would expect her to lose heat at half the rate that the pup does.
The seal example is a very simple generalization, but it does represent an important concept in a variety of situations. An African elephant is the largest living land mammal. As with the seals, the ratio of its surface area to volume determines how it exchanges internal heat with the environment. Large animals have small surface area:volume (SA:V) ratios, and in the case of elephants living in the tropics their problem is more usually one of trying not to overheat, so they are almost hairless, carry large heat radiators (their ears) and use various behaviours to promote cooling and avoid overheating. Other size-related properties affect elephants. Whilst their bulk is determined by their volume (size cubed), the compressive strength of the legs that carry this bulk around is proportional to their cross-sectional area (size squared). So large land animals have proportionally thicker legs than small animals, and this in turn determines other features of their body plan and biomechanics (see Figure 3).
Figure 3. The African elephant is the largest living land animal, and several features of its biology are linked to its size and SA:V ratio.