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Solid of revolution information


Rotating a curve. The surface formed is a surface of revolution; it encloses a solid of revolution.
Solids of revolution (Matemateca Ime-Usp)

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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Solid of revolution

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22/7 exceeds π Trapezium rule Integral of the secant function Integral of secant cubed Arclength Solid of revolution Shell integration Natural logarithm...

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Paul Guldin

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Nicolas Fatio de Duillier

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