- Thread starter
- #1

#### skatenerd

##### Active member

- Oct 3, 2012

- 114

"Let 0<r<R and x

^{2}+(y-R)

^{2}=r

^{2}be the circle centered at (0,R) of radius r. Revolving the disk enclosed by that circle about the x-axis generates a torus. Using the washer method obtain the volume of that torus."

So just a disclaimer, I have NO intention of cheating on this. I'm in the class to learn. I have gotten so far on this problem and now I'm stuck which is very frustrating since figuring out everything before now took a while. If anybody could just let me know if I did something wrong or not that would be awesome.

So far, I made a graph, and made an infinitesimally small slice through the torus, which I needed to find the area of. To do this I knew I needed the equation solved for y, so I did that and got:

y=R+(root(r

^{2}-x

^{2})) for the top half of the circle and y=R-(root(r

^{2}-x

^{2})) for the bottom half. I used the top half as the outer radius of the washer and the bottom half as the inner radius. From this I got an integral:

pi ( int (R+(root(r

^{2}-x

^{2})))^2-(R-(root(r

^{2}-x

^{2})))^2 ) dx

this ends up being:

4piR ( int (root(r

^{2}-x

^{2})) ) dx

and from there I tried using a couple different u-substitutions and nothing worked and I got frustrated, then came here. Any help would be appreciated! Thanks in advance.