## Scaling

If the sides of a cube are doubled fromtoas shown,

the surface area of the cube increases fromto– an increase by a factor ofand

the volume of the cube increases fromto– an increase by a factor of

These factors of 2 for the length,for the surface area andfor the volume are dirct consequences of the uniform scaling factor and the dimensionsfor length,for surface area andfor 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 energytimes as fast and to betimes as heavy.

In addition, physical strength is directly related to surface area (physical strength is proportional to muscle area), so increases asbut weight increases aswhich implies there is an upper mass limit at which the body cannot support it's own weight. This applies across all species.