As the title says, why divide surface area to volume for strength in living beings ? I mean why all surface area ? Shouldn't it be area touching the ground ? Thanks in advance! :)
For a given style of animal, if you double the linear dimensions, the volume increases by a factor of eight. If we assume the density is constant-people are about the density of water-the mass supported increases by a factor of eight. All that mass is supported by the leg bones. The cross section of the bones only increases by a factor of four, so the stress (which is force divided by area) is doubled.
You can see the effect of this. Large animals have much thicker legs (in proportion to body size) than small animals. This is to give more surface area to the leg bones so they can support the weight. You can't do this forever, which is why large animals tend to walk instead of jump.