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  2. Cone - Wikipedia

    en.wikipedia.org/wiki/Cone

    The lateral surface area of a right circular cone is = where is the radius of the circle at the bottom of the cone and is the slant height of the cone. [4] The surface area of the bottom circle of a cone is the same as for any circle, . Thus, the total surface area of a right circular cone can be expressed as each of the following:

  3. Hypercone - Wikipedia

    en.wikipedia.org/wiki/Hypercone

    In geometry, a hypercone (or spherical cone) is the figure in the 4-dimensional Euclidean space represented by the equation + + = It is a quadric surface, and is one of the possible 3-manifolds which are 4-dimensional equivalents of the conical surface in 3 dimensions.

  4. Solid angle - Wikipedia

    en.wikipedia.org/wiki/Solid_angle

    The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A /2 and r = 1 . The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2 θ , is the area of a spherical cap on a unit sphere

  5. 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 ...

  6. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    Archimedes showed that the surface area of a sphere is exactly four times the area of a flat disk of the same radius, and the volume enclosed by the sphere is exactly 2/3 of the volume of a cylinder of the same height and radius. Most basic formulas for surface area can be obtained by cutting surfaces and flattening them out (see: developable ...

  7. File:Cone surface area.svg - Wikipedia

    en.wikipedia.org/wiki/File:Cone_surface_area.svg

    Total surface area of a right circular cone, given its base radius 𝑟 and slant height ℓ. Source: ... given its base radius 𝑟 and slant height ℓ. ...

  8. Bicone - Wikipedia

    en.wikipedia.org/wiki/Bicone

    In geometry, a bicone or dicone (from Latin: bi-, and Greek: di-, both meaning "two") is the three-dimensional surface of revolution of a rhombus around one of its axes of symmetry. Equivalently, a bicone is the surface created by joining two congruent, right, circular cones at their bases. A bicone has circular symmetry and orthogonal ...

  9. 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 ...