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Conical (or sleevers) glasses are shaped, as the name suggests, as an inverted truncated cone around 6 inches (15 cm) tall and tapering by about 1 inch (25 mm) in diameter over its height. Also called a "shaker pint" in the United States, as the glass can be used as one half of a Boston shaker. The most common size found in the US holds 16 US ...
The Egyptians knew the correct formula for the volume of such a truncated square pyramid, but no proof of this equation is given in the Moscow papyrus. The volume of a conical or pyramidal frustum is the volume of the solid before slicing its "apex" off, minus the volume of this "apex":
Types of truncation on a square, {4}, showing red original edges, and new truncated edges in cyan. A uniform truncated square is a regular octagon, t{4}={8}. A complete truncated square becomes a new square, with a diagonal orientation. Vertices are sequenced around counterclockwise, 1-4, with truncated pairs of vertices as a and b.
A cone with a region including its apex cut off by a plane is called a truncated cone; if the truncation plane is parallel to the cone's base, it is called a frustum. [1] An elliptical cone is a cone with an elliptical base. [1] A generalized cone is the surface created by the set of lines passing through a vertex and every point on a boundary ...
The concept of cone angle is most easily visualized with symmetrical ligands, e.g. PR 3. But the approach has been refined to include less symmetrical ligands of the type PRR′R″ as well as diphosphines. In such asymmetric cases, the substituent angles' half angles, θ i / 2 , are averaged and then doubled to find the total cone angle ...
≡ 4π sr [16] – The solid angle subtended by a sphere at its centre. ≈ 12.566 37 sr: square degree: deg 2; sq.deg.; (°) 2: ≡ (π ⁄ 180) 2 sr: ≈ 0.304 62 × 10 −3 sr: steradian (SI unit) sr The solid angle subtended at the center of a sphere of radius r by a portion of the sphere having an area r 2. A sphere subtends 4π sr. [16 ...
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The surface area and the volume of the truncated icosahedron of edge length are: [2] = (+ +) = +. The sphericity of a polyhedron describes how closely a polyhedron resembles a sphere. It can be defined as the ratio of the surface area of a sphere with the same volume to the polyhedron's surface area, from which the value is between 0 and 1.