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A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) 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 presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat ...
The formula for the surface area of a sphere is more difficult to derive: because a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: A = 4πr 2 (sphere), where r is the radius of the sphere.
Specific surface area ( SSA) is a property of solids defined as the total surface area (SA) of a material per unit mass, [1] (with units of m 2 /kg or m 2 /g). Alternatively, it may be defined as SA per solid or bulk volume [2] [3] (units of m 2 /m 3 or m −1 ). It is a physical value that can be used to determine the type and properties of a ...
Surface of revolution. A portion of the curve x = 2 + cos (z) rotated around the z -axis. A torus as a square revolved around an axis along the diagonal of the square. A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the ...
Ellipsoid. An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation . An ellipsoid is a quadric surface ; that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables.
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. SA:V is an important concept in science and engineering. It is used to explain the relation between structure and function in processes occurring through the surface ...
Gabriel's horn. 3D illustration of Gabriel's horn. Torricelli's truncated acute hyperbolic solid with the added cylinder (in red) used by his proof. A Gabriel's horn (also called Torricelli's trumpet) is a type of geometric figure that has infinite surface area but finite volume. The name refers to the Christian tradition where the archangel ...
The area density (also known as areal density, surface density, superficial density, areic density, mass thickness, column density, or density thickness) of a two-dimensional object is calculated as the mass per unit area. The SI derived unit is the kilogram per square metre (kg·m −2 ). A related area number density can be defined by ...