# Relationship between radius and surface area

### Ratio of the volume and the surface area between two spheres

The surface area to volume ratio is a way of expressing the relationship x * l or x * r, in length or radius, the increase in surface area is x squared (x2) and the. In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object. But we don't have to figure out all six because we know that the top and (h is the height of the cylinder, r is the radius of the top). The surface-area-to-volume ratio, also called the surface-to-volume ratio and variously denoted sa/vol or SA:V, is the amount of surface area per unit volume of .

**Surface Area of Revolution By Integration Explained, Calculus Problems, Integral Formula, Examples**

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.

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.

## Ratio of the volume and the surface area between two spheres

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.

The length of time through which a planetary body can maintain surface-altering activity depends on how well it retains heat, and this is governed by its surface area-to-volume ratio. 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.

### Surface Area of a Sphere -- Math Fun Facts

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.

- Surface-area-to-volume ratio
- Surface Area of a Sphere

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.

## Relation of Radius, Surface Area, and Volume of a Sphere

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. 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.