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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 ...
In his work, Archimedes showed that the surface area of a cylinder is equal to: = + = (+). and that the volume of the same is: =. [3] On the sphere, he showed that the surface area is four times the area of its great circle. In modern terms, this means that the surface area is equal to:
Graphs of surface area, A against volume, V of all 5 Platonic solids and a sphere by CMG Lee, showing that the surface area decreases for rounder shapes, and the surface-area-to-volume ratio decreases with increasing volume. The dashed lines show that when the volume increases 8 (2³) times, the surface area increases 4 (2²) times.
An approximation for the volume of a thin spherical shell is the surface area of the inner sphere multiplied by the thickness t of the shell: [2] V ≈ 4 π r 2 t , {\displaystyle V\approx 4\pi r^{2}t,}
Defined by Wadell in 1935, [1] the sphericity, , of an object is the ratio of the surface area of a sphere with the same volume to the object's surface area: = where is volume of the object and is the surface area.
The surface of the spherical segment (excluding the bases) is called spherical zone. Geometric parameters for spherical segment. If the radius of the sphere is called R , the radii of the spherical segment bases are a and b , and the height of the segment (the distance from one parallel plane to the other) called h , then the volume of the ...
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