In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the axis of revolution), which may not intersect the generatrix (except at its boundary). The surface created by this revolution and which bounds the solid is the surface of revolution.
Assuming that the curve does not cross the axis, the solid's volume is equal to the length of the circle described by the figure's centroid multiplied by the figure's area (Pappus's second centroid theorem).
A representative disc is a three-dimensional volume element of a solid of revolution. The element is created by rotating a line segment (of length w) around some axis (located r units away), so that a cylindrical volume of πr2w units is enclosed.
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geometry, a solidofrevolution is a solid figure obtained by rotating a plane figure around some straight line (the axis ofrevolution), which may not...
calculating the volume of a solidofrevolutionof a solid-state material when integrating along an axis "parallel" to the axis ofrevolution. This method models...
bounded by the surface created by this revolution is the solidofrevolution. Examples of surfaces ofrevolution generated by a straight line are cylindrical...
{\displaystyle s} of the original triangle, this is: 2 s 2 3 5 . {\displaystyle {\frac {2s^{2}{\sqrt {3}}}{5}}.} The volume of the solidofrevolutionof the Koch...
volume of a right circular cylinder have been known from early antiquity. A right circular cylinder can also be thought of as the solidofrevolution generated...
for calculating the volume of a solidofrevolution, when integrating along an axis perpendicular to the axis ofrevolution. This is in contrast to disc...
of integral calculus. One of which is calculating the volume of solidsofrevolution, by rotating a plane curve around a line on the same plane. The washer...
produce most solidsofrevolution, plane surfaces and screw threads or helices. Ornamental lathes can produce three-dimensional solidsof incredible complexity...
determination of the nose cone geometrical shape for optimum performance. For many applications, such a task requires the definition of a solidofrevolution shape...
(q=a+bi+cj+dk)} results in a solidofrevolutionof the 2-dimensional Mandelbrot set around the real axis.[citation needed] Of particular interest is the...
a solidofrevolution obtained by rotating an elongated superellipse with exponent greater than 2 around its longest axis. It is a special case of superellipsoid...
22/7 exceeds π Trapezium rule Integral of the secant function Integral of secant cubed Arclength Solidofrevolution Shell integration Natural logarithm...
radar from aerodynamic forces. The shape of the nose cone must be chosen for minimum drag so a solidofrevolution is used that gives least resistance to...
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symmetry, Dihn as subgroup symmetries. In 3-dimensions, a surface or solidofrevolution has circular symmetry around an axis, also called cylindrical symmetry...
approximate a torus ofrevolution include swim rings, inner tubes and ringette rings. A torus should not be confused with a solid torus, which is formed...
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volume of a solidofrevolution. (This theorem is also known as the Pappus–Guldinus theorem and Pappus's centroid theorem, attributed to Pappus of Alexandria...
geometrical investigation of the line of briefest descent, to which is added a geometric investigation of the solidofrevolution that produces the minimum...