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Volume Of Torus

In geometry, a torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a ring torus or simply torus if the ring shape is implicit.

When the axis is tangent to the circle, the resulting surface is called a horn torus, when the axis is a chord of the circle, it is called a spindle torus. A degenerate case is when the axis is a diameter of the circle, which simply generates a 2-sphere. The ring torus bounds a solid known as a toroid. The adjective toroidal can be applied to tori, toroids or, more generally, any ring shape as in toroidal inductors and transformers. Real-world examples of (approximately) toroidal objects include doughnuts, vadais, inner tubes, bagels, many lifebuoys, O-rings and vortex rings.

2Π 2r 2t

r = tube radius, t = torus radius

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