For an rectangle of dimensions , . For an isosceles triangle with sides , and , . For an ellipse of semimajor and semiminor axes and , respectively, where is a complete elliptic integral of the second kind and is the eccentricity of the ellipse, . Ramanujan proposed the approximation . For , the ellipse simplifies to a circle, with , and the surface of revolution becomes a torus.

Pappus's second theorem gives the volume of the surface of revolution as multiplied by the area of the generating figure. For the rectangle, ellipse, and triangle, equals , , and , respectively.

Two related results are Pappus's centroid theorems, which involve surfaces generated by rotating about an axis passing through the centroid of the generating figure.

The controls enable you to choose a rectangular, elliptical or triangular cross section of varying dimensions and . Also you can vary the radius and the angle of rotation θ, up to a complete circle of 360º.