Pappus's centroid theorem

Pappus's centroid theorem (also known as the Guldinus theorem, Pappus-Guldinus theorem or Pappu's theorem) is the name of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution.

The first theorem

The first theorem states that the surface area A of a surface of revolution generated by rotating a plane curve C about an axis external to C and on the same plane is equal to product of the arc length s of C and the distance d1 traveled by its centroid.

Related Topics:
Surface area - Surface of revolution - Plane - Curve - Axis - Arc length - Centroid

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:A = sd_1.,

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For example, the surface area of the torus with minor radius r and major radius R is

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:A = (2pi r)(2pi R) = 4pi^2 R r.,

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