# Relationship of surface area and volume

### Surface-area-to-volume ratio - Wikipedia

Imagine a cube 1 foot on a side (substitute “meter” for “foot” if you like). Its volume will be 1 cubic foot. Each side is one square foot, so its total surface area is 6. The same uncertainty exists when trying to relate surface area to volume. k Views What is the relationship between area and volume? 8, Views. A: Surface area to volume ratio can be found easily for several simple shapes, like for example a cube or a sphere. For a cube, the equation for surface area is.

February See also: Dust explosion Materials with high surface area to volume ratio e. Examples include grain dust; while grain isn't typically flammable, grain dust is explosive.

Finely ground salt dissolves much more quickly than coarse salt. High surface area to volume ratio provides a strong "driving force" to speed up thermodynamic processes that minimize free energy. Biology[ edit ] Cells lining the small intestine increase the surface area over which they can absorb nutrients with a carpet of tuftlike microvilli.

The ratio between the surface area and volume of cells and organisms has an enormous impact on their biologyincluding their physiology and behavior. For example, many aquatic microorganisms have increased surface area to increase their drag in the water. This reduces their rate of sink and allows them to remain near the surface with less energy expenditure.

## Surface-area-to-volume ratio

The finely-branched appendages of filter feeders such as krill provide a large surface area to sift the water for food. More contact with the environment through the surface of a cell or an organ relative to its volume increases loss of water and dissolved substances. High surface area to volume ratios also present problems of temperature control in unfavorable environments. This is true for cubes, spheres, or any other object whose size is increased without changing its shape.

For cubes smaller than this, surface area is greater relative to volume than it is in larger cubes where volume is greater relative to surface area.

Surface area and volume of a cube

Sometimes a graph that shows how the relationship between two variables changes is more instructive. For example, a graph of the ratio of surface area to volume,clearly illustrates that as the size of an object increases without changing shapethis ratio decreases.

### The surface area to volume relationship

Mathematically, that tells us that the denominator volume increases faster relative to the numerator surface area as object size increases. Organisms exhibit a variety of modifications, both physiological and anatomical, to compensate for changes in the surface area to volume ratio associated with size differences.

One example of this is the higher metabolic rates found in smaller homeothermic animals. Because of their large surface area relative to volume, small animals lose heat at much higher rates than large animals, and therefore must produce more heat to offset the effects of thermal conductance.

Another example is the variety of internal transport systems that have developed in plants and animals for actively moving materials throughout the organism, thus enabling them to circumvent the limits imposed by passive diffusion. Many organisms have developed structures that actually increase their surface area: Graph the surface areas x axis and volumes y axis of these spheres on a standard plot and a log-log plot.