Surface-area-to-volume ratio

The surface area to volume ratio of an object is the relationship between two measurements. It is the ratio of Surface area to volume. It shows the comparison between the size of the outside of an object and the amount inside. Small or thin objects have a large surface area compared to the volume. This gives them a large ratio of surface to volume. Larger objects have small surface area compared to the volume so they have a small surface area to volume ratio. A large lump, for example, has a small ratio, and may be smashed into powder to give it a large surface to volume ratio.

Two common ways of writing it are sa/vol or SA:V. Either of these say to divide the surface area by the volume. This shows how much surface area is required for each unit of volume.

Example

Cube 1 measures 1 meter on each side. It has a surface area of 6 m². Surface area = length x length (or length²) multiplied by the number of sides (6). It has a volume of 1 cubic meter. Volume = length x length x length or length³. Its ratio is 6 m² per cubic meter.
Cube 2 had sides that measured 10m Its surface area is 10² x 6 = 600 m² Its volume is 1000 cubic meters Its ratio is 0.6 m² per cubic meter.

Surface-area-to-volume Ratio Media

Graphs of surface area, A against volume, V of the Platonic solids and a sphere, showing that the surface area decreases for rounder shapes, and the surface-area-to-volume ratio decreases with increasing volume. Their intercepts with the dashed lines show that when the volume increases 8 (2³) times, the surface area increases 4 (2²) times.
Plot of the surface-area:volume ratio (SA:V) for a 3-dimensional ball, showing the ratio decline inversely as the radius of the ball increases.
Cells lining the small intestine increase the surface area over which they can absorb nutrients with a carpet of tuftlike microvilli.
Image d'un tétraèdre
Image d'un cube
Picture of an octahedron
Image d'un dodécaèdre
Cylinder with height=2*radius and enclosed by 2 hemispheres
Image d'un icosaèdre, un des solides de Platon
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