# Relationship between diameter and surface area

### Surface-area-to-volume ratio - Wikipedia The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the. NOTE: The value of π can never be calculated exactly, so the surface area of a sphere is only a approximation. Surface area of sphere in terms of diameter = πd . According to below table, One sample (D) has greatest surface area but other sample (C) has smallest average pore diameter. I can't realize what relationship.

## Surface-area-to-volume ratio

We'll begin with a reminder of some basic geometric formulae. The surface area and volume of a cube can be found with the following equations: The equations for the surface area and volume of a sphere are: For example, when length is doubled i. The increase in volume is always greater than the increase in surface area. 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.

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.

### Surface area - Wikipedia

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.

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

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. Fire spread behavior is frequently correlated to the surface-area-to-volume ratio of the fuel e. The higher its value, the faster a particle responds to changes in environmental conditions, such as temperature or moisture.

Higher values are also correlated to shorter fuel ignition times, and hence faster fire spread rates. Planetary cooling[ edit ] A body of icy or rocky material in outer space may, if it can build and retain sufficient heat, develop a differentiated interior and alter its surface through volcanic or tectonic activity.