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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 (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.

  3. Cylinder - Wikipedia

    en.wikipedia.org/wiki/Cylinder

    This formula holds whether or not the cylinder is a right cylinder. [7] This formula may be established by using Cavalieri's principle. A solid elliptic right cylinder with the semi-axes a and b for the base ellipse and height h. In more generality, by the same principle, the volume of any cylinder is the product of the area of a base and the ...

  4. List of formulas in elementary geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),

  5. Sphere–cylinder intersection - Wikipedia

    en.wikipedia.org/wiki/Spherecylinder_intersection

    If the sphere is smaller than the cylinder (<) and + =, the sphere lies in the interior of the cylinder except for one point. The intersection is the single point ( r , 0 , 0 ) {\displaystyle (r,0,0)} .

  6. Intersection curve - Wikipedia

    en.wikipedia.org/wiki/Intersection_curve

    In the third case, the sphere and cylinder touch each other at one singular point. The intersection curve is self-intersecting. If the cylinder and sphere have the same radius and the midpoint of the sphere is located on the axis of the cylinder, then the intersection curve consists of singular points (a circle) only.

  7. Sphere - Wikipedia

    en.wikipedia.org/wiki/Sphere

    The volume and area formulas were first determined in Archimedes's On the Sphere and Cylinder by the method of exhaustion. Zenodorus was the first to state that, for a given surface area, the sphere is the solid of maximum volume.

  8. List of centroids - Wikipedia

    en.wikipedia.org/wiki/List_of_centroids

    The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.

  9. 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 ...