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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.
For example, two capsules intersect if the distance between the capsules' segments is smaller than the sum of their radii. This holds for arbitrarily rotated capsules, which is why they're more appealing than cylinders in practice. A bounding cylinder is a cylinder containing the object. In most applications the axis of the cylinder is aligned ...
A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids, prisms (and other polyhedrons), cubes, cylinders, cones (and truncated cones). [2]
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 ...
The volume of an ungula of a cylinder was calculated by Grégoire de Saint Vincent. [2] Two cylinders with equal radii and perpendicular axes intersect in four double ungulae. [3] The bicylinder formed by the intersection had been measured by Archimedes in The Method of Mechanical Theorems, but the manuscript was lost until 1906.
A cylindric section is the intersection of a cylinder's surface with a plane. They are, in general, curves and are special types of plane sections. The cylindric section by a plane that contains two elements of a cylinder is a parallelogram. [4] Such a cylindric section of a right cylinder is a rectangle. [4]
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.