Thread: Spherical Parametrization for volume calculation - Your help needed.

Hi - I'm stuck on a problem to find the volume of a Tori/Torus. I can find a 2 variable parameterization (which allows me to compute the surface area by double integral for the first part of the question) but cant find a way to set it in 3 (spherical coords) to compute the volume.

The equation of the shape is:



If anyone can help me out with the transformation to spherical and intervals I'd appreciate it...

Thanks, F

A parameterization for the torus is given by
, where .

Here R is the major radius and s is the minor radius. Basically you can construct this parameterization by beginning with the large circle .
This parameterization can be extended to the torus by adding smaller circles of radius s at each point.

By the way, you can calculate the volume of a torus simply by transforming it into a cylinder. Given a major radius R its height is then 2 pi R and the base has a surface of pi s^2 where s is the minor radius.