If the sides of a cube are doubled from
to
as shown,
the surface area of the cube increases from
to
– an increase by a factor of
and
the volume of the cube increases from
to
– an increase by a factor of
These factors of 2 for the length,for the surface area and
for the volume are dirct consequences of the uniform scaling factor and the dimensions
for length,
for surface area and
for volume.
Any quantity directly related to the area or volume will scale in the same way.
The rate of thermal energy loss is directly related to the area so will increase as
The mass is directly related to the volume so will increase as
The two quantities above – rate of thermal energy loss and mass – can be directly related to living objects, both across and within species. We would expect a person 1.3 times as tall to lose thermal energy
times as fast and to be
times as heavy.
In addition, physical strength is directly related to surface area (physical strength is proportional to muscle area), so increases as
but weight increases as
which implies there is an upper mass limit at which the body cannot support it's own weight. This applies across all species.