HTML code for site/blog
Appearance
Sample
StudyMath

# Torus

Anton2008-11-25 19:52:15
A torus has the shape of a doughnut. Formally, a torus is a surface of revolution generated by revolving a circle in three dimensional space about a line which does not intersect the circle.

Torus surface area and volume are calculated by the Pappus's centroid theorems:

$A = s d$, where s - the arc length of the curve being rotated, d is the distance traveled by the centroid of the region in one rotation,
$V = A d$, where A - area of the region being rotated, d is the distance traveled by the centroid of the region in one rotation,

So surface area of torus: $S = (2\pi r)(2\pi R) = 4 \pi^2 Rr$
Torus volume: $V = (\pi r^2)(2\pi R)=2 \pi^2 R r^2$
Torus
Surface area:
Volume:

The three different classes of standard tori correspond to the three possible relative sizes of r and R. When R > r, the surface will be the standard ring torus. The case R = r corresponds to the horn torus, which in effect is a torus with no "hole". The case R < r describes a self-intersecting surface called a spindle torus.

### Not suitable?

View all calculators
(240 calculators in total. )
Request a calculator