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  2. On the Sphere and Cylinder - Wikipedia

    en.wikipedia.org/wiki/On_the_Sphere_and_Cylinder

    The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes. The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder.

  3. List of centroids - Wikipedia

    en.wikipedia.org/wiki/List_of_centroids

    Quarter-circular arc The points on the circle x 2 + y 2 = r 2 {\displaystyle \,\!x^{2}+y^{2}=r^{2}} and in the first quadrant 2 r π {\displaystyle {\frac {2r}{\pi }}}

  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. List of formulas in elementary geometry - Wikipedia

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

    Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities; List of volume formulas – Quantity of three-dimensional space

  6. Napkin ring problem - Wikipedia

    en.wikipedia.org/wiki/Napkin_ring_problem

    In this case the volume of the band is the volume of the whole sphere, which matches the formula given above. An early study of this problem was written by 17th-century Japanese mathematician Seki Kōwa. According to Smith & Mikami (1914), Seki called this solid an arc-ring, or in Japanese kokan or kokwan. [1]

  7. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    An example of a spherical cap in blue (and another in red) 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.

  8. Spherical sector - Wikipedia

    en.wikipedia.org/wiki/Spherical_sector

    If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is =. This may also be written as V = 2 π r 3 3 ( 1 − cos ⁡ φ ) , {\displaystyle V={\frac {2\pi r^{3}}{3}}(1-\cos \varphi )\,,} where φ is half the cone angle, i.e., φ is the angle between the rim of the cap and the direction ...

  9. Centroid - Wikipedia

    en.wikipedia.org/wiki/Centroid

    The centroid of many figures (regular polygon, regular polyhedron, cylinder, rectangle, rhombus, circle, sphere, ellipse, ellipsoid, superellipse, superellipsoid, etc.) can be determined by this principle alone. In particular, the centroid of a parallelogram is the meeting point of its two diagonals. This is not true of other quadrilaterals.

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