Final answer:
The relationship between the surface area of a cube to its side length is an example of direct variation, where the surface area increases proportionally with the increase in side length.
Step-by-step explanation:
The relationship between the surface area of a cube (SA) to its side length (s) is an example of a mathematical concept known as direct variation. When considering two cubes of different sizes, the surface area of each cube is calculated using the formula SA = 6s², where 's' is the length of a side of the cube. As the side length increases, the surface area increases proportionally. For instance, a cube with a side length of 1 cm will have a surface area of 6 cm², while a cube with a side length of 3 cm will have a much larger surface area of 54 cm².
This concept is important not just in pure mathematics, but also in fields such as chemistry and biology, where the surface area to volume ratio has significant implications. For example, the surface area to volume ratio affects the rate at which cells can exchange materials with their surroundings and is a limiting factor on cell size.