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  2. 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 ...

  3. Right circular cylinder - Wikipedia

    en.wikipedia.org/wiki/Right_circular_cylinder

    Illustration of a cylinder and the planification of its lateral surface. The lateral surface of a right cylinder is the meeting of the generatrices. [3] It can be obtained by the product between the length of the circumference of the base and the height of the cylinder.

  4. Capsule (geometry) - Wikipedia

    en.wikipedia.org/wiki/Capsule_(geometry)

    The volume of a capsule is calculated by adding the volume of a ball of radius (that accounts for the two hemispheres) to the volume of the cylindrical part. Hence, if the cylinder has height h {\displaystyle h} ,

  5. List of formulas in elementary geometry - Wikipedia

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

    Area#Area formulas – Size of a two-dimensional surface; 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

  6. 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 ...

  7. Volume element - Wikipedia

    en.wikipedia.org/wiki/Volume_element

    In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form = (,,) where the are the coordinates, so that the volume of any set can be computed by ⁡ = (,,).

  8. 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.

  9. Shell integration - Wikipedia

    en.wikipedia.org/wiki/Shell_integration

    The shell method goes as follows: Consider a volume in three dimensions obtained by rotating a cross-section in the xy-plane around the y-axis. Suppose the cross-section is defined by the graph of the positive function f(x) on the interval [a, b]. Then the formula for the volume will be: ()