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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 ...
The sphere has the smallest surface area of all surfaces that enclose a given volume, and it encloses the largest volume among all closed surfaces with a given surface area. [11] The sphere therefore appears in nature: for example, bubbles and small water drops are roughly spherical because the surface tension locally minimizes surface area.
For a rhombicosidodecahedron with edge length a, its surface area and volume are: = ... Editable printable net of a Rhombicosidodecahedron with interactive 3D view;
=, and the surface area of the sphere is =. Another type of sphere arises from a 4-ball, whose three-dimensional surface is the 3-sphere : points equidistant to the origin of the euclidean space R 4 .
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables is the radius, = is the circumference (the length of any one of its great circles), is the surface area,
Direct projection of 3-sphere into 3D space and covered with surface grid, showing structure as stack of 3D spheres (2-spheres) In mathematics , a hypersphere , 3-sphere , or glome is a 4-dimensional analogue of a sphere , and is the 3-dimensional n -sphere .
The surface area of a parallelepiped is the sum of the areas of the ... D 3d order 12 D 2h order 8 C 2h ... A formula to compute the volume of an n ...
The surface area of a regular tetrahedron is four times the area of an equilateral triangle: [6] = =. The height of a regular tetrahedron is 6 3 a {\textstyle {\frac {\sqrt {6}}{3}}a} . [ 7 ] The volume of a regular tetrahedron can be ascertained similarly as the other pyramids, one-third of the base and its height.
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