By contrast, objects with acute-angled spikes will have very large surface area for a given volume.įor solid spheres 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.Ī solid sphere or ball is a three-dimensional object, being the solid figure bounded by a sphere. įor a given volume, the object with the smallest surface area (and therefore with the smallest SA:V) is a ball, a consequence of the isoperimetric inequality in 3 dimensions. ![]() Similar explanation appears in the literature: "Small size implies a large ratio of surface area to volume, thereby helping to maximize the uptake of nutrients across the plasma membrane", and elsewhere. The relation between SA:V and diffusion or heat conduction rate is explained from flux and surface perspective, focusing on the surface of a body as the place where diffusion, or heat conduction, takes place, i.e., the larger the SA:V there is more surface area per unit volume through which material can diffuse, therefore, the diffusion or heat conduction, will be faster. SA:V is used to explain the diffusion of small molecules, like oxygen and carbon dioxide between air, blood and cells, water loss by animals, bacterial morphogenesis, organism's thermoregulation, design of artificial bone tissue, artificial lungs and many more biological and biotechnological structures. Good examples for such processes are processes governed by the heat equation, that is, diffusion and heat transfer by thermal conduction. It is used to explain the relation between structure and function in processes occurring through the surface and the volume. SA:V is an important concept in science and engineering. ![]() The surface-area-to-volume ratio or surface-to-volume ratio (denoted as SA:V, SA/V, or sa/vol) is the ratio between surface area and volume of an object or collection of objects. Their intercepts with the dashed lines show that when the volume increases 8 (2³) times, the surface area increases 4 (2²) times. Surface area per unit volume 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.
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