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  2. Sphere - Wikipedia

    en.wikipedia.org/wiki/Sphere

    A sphere of radius r has area element = ⁡. This can be found from the volume element in spherical coordinates with r held constant. [9] A sphere of any radius centered at zero is an integral surface of the following differential form: + + =

  3. Wigner–Seitz radius - Wikipedia

    en.wikipedia.org/wiki/Wigner–Seitz_radius

    The Wigner–Seitz radius, named after Eugene Wigner and Frederick Seitz, is the radius of a sphere whose volume is equal to the mean volume per atom in a solid (for first group metals). [1] In the more general case of metals having more valence electrons, r s {\displaystyle r_{\rm {s}}} is the radius of a sphere whose volume is equal to the ...

  4. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    The volume is thus the difference between sphere 2's cap ... For example, assuming the Earth is a sphere of radius 6371 km, the surface area of the arctic ...

  5. Volume of an n-ball - Wikipedia

    en.wikipedia.org/wiki/Volume_of_an_n-ball

    The volume can be computed without use of the Gamma function. As is proved below using a vector-calculus double integral in polar coordinates, the volume V of an n-ball of radius R can be expressed recursively in terms of the volume of an (n − 2)-ball, via the interleaved recurrence relation:

  6. On the Sphere and Cylinder - Wikipedia

    en.wikipedia.org/wiki/On_the_Sphere_and_Cylinder

    On the Sphere and Cylinder (Greek: Περὶ σφαίρας καὶ κυλίνδρου) is a treatise that was published by Archimedes in two volumes c. 225 BCE. [1] It most notably details how to find the surface area of a sphere and the volume of the contained ball and the analogous values for a cylinder, and was the first to do so. [2]

  7. Spherical segment - Wikipedia

    en.wikipedia.org/wiki/Spherical_segment

    Thus, the segment volume equals the sum of three volumes: two right circular cylinders one of radius a and the second of radius b (both of height /) and a sphere of radius /. The curved surface area of the spherical zone—which excludes the top and bottom bases—is given by =.

  8. Equivalent radius - Wikipedia

    en.wikipedia.org/wiki/Equivalent_radius

    A sphere (top), rotational ellipsoid (left) and triaxial ellipsoid (right) The volume of a sphere of radius R is . Given the volume of a non-spherical object V, one can calculate its volume-equivalent radius by setting = or, alternatively:

  9. n-sphere - Wikipedia

    en.wikipedia.org/wiki/N-sphere

    The formula for the volume of the ⁠ ⁠-ball can be derived from this by integration. Similarly the surface area element of the ⁠ ⁠-sphere of radius ⁠ ⁠, which generalizes the area element of the ⁠ ⁠-sphere, is given by