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An annulus Illustration of Mamikon's visual calculus method showing that the areas of two annuli with the same chord length are the same regardless of inner and outer radii. [1] In mathematics, an annulus (pl.: annuli or annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware washer.
Disc integration, also known in integral calculus as the disc method, is a method for calculating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution. This method models the resulting three-dimensional shape as a stack of an infinite number of discs of varying radius ...
Shell integration (the shell method in integral calculus) is a method for calculating the volume of a solid of revolution, when integrating along an axis perpendicular to the axis of revolution. This is in contrast to disc integration which integrates along the axis parallel to the axis of revolution.
Two common methods for finding the volume of a solid of revolution are the disc method and the shell method of integration.To apply these methods, it is easiest to draw the graph in question; identify the area that is to be revolved about the axis of revolution; determine the volume of either a disc-shaped slice of the solid, with thickness δx, or a cylindrical shell of width δx; and then ...
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.
Belleville washer. A Belleville washer, also known as a coned-disc spring, [1] conical spring washer, [2] disc spring, Belleville spring or cupped spring washer, is a conical shell which can be loaded along its axis either statically or dynamically. A Belleville washer is a type of spring shaped like a washer.
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 ...
On a screw, the bearing area loosely refers to the underside of the head. [1] Strictly speaking, the bearing area refers to the area of the screw head that directly bears on the part being fastened. [2] For a cylindrical bearing, it is the projected area perpendicular to the applied force. [3]