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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. [1] 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 ...
A sphere is the surface of a solid ball, here having radius r. In mathematics, a surface is a mathematical model of the common concept of a surface.It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line.
The integral edge lengths of a Heronian tetrahedron with this volume and surface area are 25, 39, 56, 120, 153 and 160. [ 6 ] In 1943, E. P. Starke published another example, in which two faces are isosceles triangles with base 896 and sides 1073, and the other two faces are also isosceles with base 990 and the same sides. [ 7 ]
Their intercepts with the dashed lines show that when the volume increases 8 (2³) times, the surface area increases 4 (2²) times. 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.
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 ).
The blue area above the x-axis may be specified as positive area, while the yellow area below the x-axis is the negative area. The integral of a real function can be imagined as the signed area between the x {\displaystyle x} -axis and the curve y = f ( x ) {\displaystyle y=f(x)} over an interval [ a , b ].
For example, assuming the Earth is a sphere of radius 6371 km, the surface area of the arctic (north of the Arctic Circle, at latitude 66.56° as of August 2016 [7]) is 2π ⋅ 6371 2 | sin 90° − sin 66.56° | = 21.04 million km 2 (8.12 million sq mi), or 0.5 ⋅ | sin 90° − sin 66.56° | = 4.125% of the total surface area of the Earth.
A minimal surface is defined not as a surface of minimal area, but as a surface with a mean curvature of 0. [2] Since a mean curvature of 0 is a necessary condition of a surface of minimal area, all minimal surfaces of revolution are minimal surfaces, but not all minimal surfaces are minimal surfaces of revolution.