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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 ...
Green line has two intersections. Yellow line lies tangent to the cylinder, so has infinitely many points of intersection. Line-cylinder intersection is the calculation of any points of intersection, given an analytic geometry description of a line and a cylinder in 3d space. An arbitrary line and cylinder may have no intersection at all.
The California Subject Examinations for Teachers, also abbreviated as CSET, is a group of subject matter tests used in California and other states to assess mastery of subject matter content by prospective K-12 teachers.
The intersection of two planes. The analytic determination of the intersection curve of two surfaces is easy only in simple cases; for example: a) the intersection of two planes, b) plane section of a quadric (sphere, cylinder, cone, etc.), c) intersection of two quadrics in special cases. For the general case, literature provides algorithms ...
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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].
In the 3rd century BC, Archimedes, using a method resembling Cavalieri's principle, [5] was able to find the volume of a sphere given the volumes of a cone and cylinder in his work The Method of Mechanical Theorems. In the 5th century AD, Zu Chongzhi and his son Zu Gengzhi established a similar method to find a sphere's volume. [2]
Between them, an announced result concerned the volume of the intersection of two cylinders, a figure that Apostol and Mnatsakanian have renamed n = 4 Archimedean globe (and the half of it, n = 4 Archimedean dome), whose volume relates to the n-polygonal pyramid.