Search results
Results from the WOW.Com Content Network
The equilateral cylinder is characterized by being a right circular cylinder in which the diameter of the base is equal to the value of the height (geratrix). [ 4 ] Then, assuming that the radius of the base of an equilateral cylinder is r {\displaystyle r\,} then the diameter of the base of this cylinder is 2 r {\displaystyle 2r\,} and its ...
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
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 ...
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.
V is the total wetted volume of the channel, S is the total wetted surface area. This definition is reduced to 4 A P {\displaystyle {\frac {4A}{P}}} for uniform non-circular cross-section channels, and 2 R {\displaystyle 2R} for circular pipes.
The cube's volume is / (+) times that of the dodecahedron's. [63] In fact, golden rectangles inside a dodecahedron are in golden proportions to an inscribed cube, such that edges of a cube and the long edges of a golden rectangle are themselves in φ : φ 2 {\displaystyle \textstyle \varphi \mathbin {:} \varphi ^{2}} ratio.
Given that A is the area of the triangular prism's base, and the three heights h 1, h 2, and h 3, its volume can be determined in the following formula: [14] (+ +). Schönhardt polyhedron. Schönhardt polyhedron is another polyhedron constructed from a triangular prism with equilateral triangle bases.
A sphere has 2/3 the volume and surface area of its circumscribing cylinder. A sphere and cylinder were placed on the tomb of Archimedes at his request. Archimedes (c. 287 BCE – c. 212 BCE), a colorful figure about whom many historical anecdotes are recorded, is remembered along with Euclid as one of the greatest of ancient mathematicians.