# Thread: Disks, Washers, Shells and Confusion

1. ## Disks, Washers, Shells and Confusion

Hello Everyone,

I'm currently taking a calculus 2 course and I don't really understand the differences between the disk method for finding the soild of revolution and the washer and shells methods. I gather that the shells method is easier when you are rotatating around the y axis and disk is better when rotating around the x axis. Washers seems to be good for when there will be a hole in the object that you are rotating. My problem is that I don't really know how to use these methods and have been stuck for hours now trying to apply them.

Thanks a lot.

2. Your post borders upon asking for a tutorial and we are not a tutorial service.
If you will post a specific question telling us what you do not understand, then perhaps someone can help.

3. No, those rules will not get you very far. Each method is better when it is. The very best method is the one you understand. It would behoove you to practice both.

Let's see what you have.

4. Thanks for the quick replies. I have x-y^2=16, x=20 rotated about x=0. I set y^2 +16=20 and solved for the roots and got \pm2. I then integrated \pi x (y^2 +16)^2 dy. The correct answer is 5888\pi/15 and I have 18112\pi /15. Is my logic correct? I've checked and double checked my work and I can't find a mistake which leads me to believe that I'm doing something wrong in the setup.

Thanks again

$\displaystyle V = 2\pi \int_0^2 20^2 - (y^2+16)^2 \, dy$

6. Do you also have to solve the corresponding integral from -2 to 0 and add the results together?

Do you also have to solve the corresponding integral from -2 to 0 and add the results together?
note the $\displaystyle 2\pi$ in front of the integral ... as stated, I took advantage of the graph's symmetry.

8. Ah, I was also confused by the 2\pi part, thanks a lot

9. Got the answer, thanks so much Skeeter!

10. Or...

$\displaystyle 4\cdot\pi\int_{16}^{20}x\cdot\sqrt{x-16}\;dx$

More symmetry creates the slightly unusual value on the front.

Excellent example. Which do you perceive as easier or more useful? It masy be one or the other for this problem, but a different choice on the next.