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  2. Sphere - Wikipedia

    en.wikipedia.org/wiki/Sphere

    where r is the radius and d is the diameter of the sphere. Archimedes first derived this formula by showing that the volume inside a sphere is twice the volume between the sphere and the circumscribed cylinder of that sphere (having the height and diameter equal to the diameter of the sphere). [6]

  3. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    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.

  4. 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:

  5. Equivalent radius - Wikipedia

    en.wikipedia.org/wiki/Equivalent_radius

    In applied sciences, the equivalent radius (or mean radius) is the radius of a circle or sphere with the same perimeter, area, or volume of a non-circular or non-spherical object. The equivalent diameter (or mean diameter ) ( D {\displaystyle D} ) is twice the equivalent radius.

  6. 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 =.

  7. On the Sphere and Cylinder - Wikipedia

    en.wikipedia.org/wiki/On_the_Sphere_and_Cylinder

    The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes. The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder.

  8. n-sphere - Wikipedia

    en.wikipedia.org/wiki/N-sphere

    The 3-sphere is the boundary of a ⁠ ⁠-ball in four-dimensional space. The ⁠ ⁠-sphere is the boundary of an ⁠ ⁠-ball. Given a Cartesian coordinate system, the unit ⁠ ⁠-sphere of radius ⁠ ⁠ can be defined as:

  9. Spherical shell - Wikipedia

    en.wikipedia.org/wiki/Spherical_shell

    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,}