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:
, where s is for the arc length of the curve being rotated, d is for the distance traveled by the centroid of the region in one rotation,
, where A is for area of the region being rotated, d is for the distance traveled by the centroid of the region in one rotation,
So surface area of torus:
Distance from the center of the tube to the center of the torus
Save the calculation to reuse next time, to extension embed in your website or share share with friends.
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.