Calculating Surface Area of a Torus

[stonecoldgen]

So the first question is to find the surface area of a torus generated by rotating the circle (or shall I say semi circle) y=√r-x² around y=r

if the idea is to find the surface are of the half torus and then multiply by 2, wouldn't it be the same for the circle (or shall I say semi circle, again) rotated around x=r?


Thanks.

 

[Dick]

No, I don't think so. If you rotate the same semicircle around the two different axes the surfaces look pretty different, don't they? One looks like the upper half of a full torus, the other looks like the inner half of a full torus. Don't think they are equal in area.