[SPLIT] Find the volume of the torus formed by rotating...

[Pre]

Find the volume of the torus formed by rotating the region bounded by x^2 + y^2 = 9 about x=3.

Now when I solve for y I got positive or negative sqrt(9-x^2).

I was also wondering if it would be easier to solve for x instead because then I just need 1 integral for the upper - lower. I'm just stumped.

 

[skeeter]

you could use cylindrical shells ...

\(\displaystyle \L V = 2\pi \int_{-3}^3 (3-x)(2\sqrt{9-x^2}) dx\)

or the theorem of Pappus ...

\(\displaystyle \L V = \pi r^2 \cdot 2\pi R\) where r = circle radius and R = rotation radius of the circle's centroid.

both should yield the same result.