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  2. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle ), so that the height of the cap is equal to the radius of the sphere, the spherical ...

  3. Spherical sector - Wikipedia

    en.wikipedia.org/wiki/Spherical_sector

    In geometry, a spherical sector, [ 1] also known as a spherical cone, [ 2] is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap. It is the three-dimensional analogue of ...

  4. 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]

  5. Sphere - Wikipedia

    en.wikipedia.org/wiki/Sphere

    Sphere. A sphere (from Greek σφαῖρα, sphaîra) [ 1] is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. [ 2]

  6. Shell theorem - Wikipedia

    en.wikipedia.org/wiki/Shell_theorem

    There are three steps to proving Newton's shell theorem (1). First, the equation for a gravitational field due to a ring of mass will be derived. Arranging an infinite number of infinitely thin rings to make a disc, this equation involving a ring will be used to find the gravitational field due to a disk.

  7. 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], when t is very small compared to r (). The total surface area of the spherical shell is .

  8. Spherical segment - Wikipedia

    en.wikipedia.org/wiki/Spherical_segment

    Terminology for spherical segments. In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes . It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum. The surface of the spherical segment (excluding the bases) is called spherical zone .

  9. Spherical wedge - Wikipedia

    en.wikipedia.org/wiki/Spherical_wedge

    Spherical wedge. In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge's base ). The angle between the radii lying within the bounding semidisks is the dihedral α. If AB is a semidisk that forms a ball when completely revolved about the z -axis, revolving AB only ...