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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. The Method of Mechanical Theorems - Wikipedia

   en.wikipedia.org/wiki/The_Method_of_Mechanical...

   [1]: 20-21 There are no details given for the argument, but the obvious reason is that the cone can be divided into infinitesimal cones by splitting the base area up, and then each cone makes a contribution according to its base area, just the same as in the sphere. Let the surface of the sphere be S.

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. 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. Cone (topology) - Wikipedia

   en.wikipedia.org/wiki/Cone_(topology)

   The cone over a closed interval I of the real line is a filled-in triangle (with one of the edges being I), otherwise known as a 2-simplex (see the final example). The cone over a polygon P is a pyramid with base P. The cone over a disk is the solid cone of classical geometry (hence the concept's name). The cone over a circle given by

7. 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 ...

8. Packing problems - Wikipedia

   en.wikipedia.org/wiki/Packing_problems

   Packing different rectangles in a rectangle: The problem of packing multiple rectangles of varying widths and heights in an enclosing rectangle of minimum area (but with no boundaries on the enclosing rectangle's width or height) has an important application in combining images into a single larger image. A web page that loads a single larger ...

9. Cone (algebraic geometry) - Wikipedia

   en.wikipedia.org/wiki/Cone_(algebraic_geometry)

   In algebraic geometry, a cone is a generalization of a vector bundle. Specifically, given a scheme X , the relative Spec C = Spec X ⁡ R {\displaystyle C=\operatorname {Spec} _{X}R}