I have a ring torus of the following proportions illustrated in the diagram below.

The diagram shows a cross section of the torus (it is not proportional)

Inner hole radius = a = 5.920118575210524

tube radius = r = 82.983609982018226

I am interested in surface areas.

I know how to calculate the total surface area of the torus.

But how can I calculate the area of any horizontal strip of the surface?

I have a specific example in mind, although I would like to know the methodology too.

In the diagram there is a strip labelled d, which runs from the inner equator to a point which is c degrees above.

I have worked out that:

d=15

Therefore c = 10.3567040

How can I calculate the surface area of the torus that this strip ‘d’ covers as it rotates 360 degrees around the y axis?

I will appreciate any help anyone can give.

Thanks,

Tom