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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 ...
A right frustum is a right pyramid or a right cone truncated perpendicularly to its axis; [3] otherwise, it is an oblique frustum. In a truncated cone or truncated pyramid, the truncation plane is not necessarily parallel to the cone's base, as in a frustum.
Quarter-circular area [2] ... Right circular solid cone: r = the radius of the cone's base h = the distance is from base to the apex Solid sphere ...
For example, assuming the Earth is a sphere of radius 6371 km, the surface area of the arctic (north of the Arctic Circle, at latitude 66.56° as of August 2016 [7]) is 2π ⋅ 6371 2 | sin 90° − sin 66.56° | = 21.04 million km 2 (8.12 million sq mi), or 0.5 ⋅ | sin 90° − sin 66.56° | = 4.125% of the total surface area of the Earth ...
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.
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 ),
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 ...
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