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  2. On the Sphere and Cylinder - Wikipedia

    en.wikipedia.org/wiki/On_the_Sphere_and_Cylinder

    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 ...

  3. Surface area - Wikipedia

    en.wikipedia.org/wiki/Surface_area

    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 ...

  4. Pappus's centroid theorem - Wikipedia

    en.wikipedia.org/wiki/Pappus's_centroid_theorem

    The theorem applied to an open cylinder, cone and a sphere to obtain their surface areas. The centroids are at a distance a (in red) from the axis of rotation.. In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of ...

  5. Right circular cylinder - Wikipedia

    en.wikipedia.org/wiki/Right_circular_cylinder

    Illustration of a cylinder. A right circular cylinder is a cylinder whose generatrices are perpendicular to the bases. Thus, in a right circular cylinder, the generatrix and the height have the same measurements. [1] It is also less often called a cylinder of revolution, because it can be obtained by rotating a rectangle of sides and around one ...

  6. Cylinder - Wikipedia

    en.wikipedia.org/wiki/Cylinder

    A cylinder is defined as a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line. [12] Such cylinders have, at times, been referred to as generalized cylinders.

  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. Steinmetz solid - Wikipedia

    en.wikipedia.org/wiki/Steinmetz_solid

    The generation of a bicylinder Calculating the volume of a bicylinder. A bicylinder generated by two cylinders with radius r has the volume =, and the surface area [1] [6] =.. The upper half of a bicylinder is the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous formulas calculating the volume ...

  9. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    The formula for the surface area of a sphere is more difficult to derive: because a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: [6] A = 4πr 2 (sphere), where r is the radius of the sphere.