# Washer method and disc method for finding volumes of graphs

1. Mar 6, 2005

### KataKoniK

Hi,

I was wondering how do you know which method to use when let's say, they give you two equations and say to find the volume of the solid rotated on a certain axis. Is there a certain rule of thumb to follow (like in stock market - buy low sell high?)? I am really confused.

2. Mar 6, 2005

### Jameson

depends on how the equation are given to you.

Try this one using the disc method.

Revolve $y = x^3-x$ about the y-axis. You can't. Use which one is more comfortable and which one makes sense.

Last edited: Mar 6, 2005
3. Mar 6, 2005

### DoubleMike

You could do any problem either way... But some are easier to solve using a particular method.

y=x^3 - x can be solved with disks but you have to integrate in respect to y rather than x...

Makes it a bit more complex.

4. Mar 6, 2005

### mathwonk

having answered this question in utter and exhaustive detail, months ago, I wonder, is there some way we could arrange for students to search our site for answers that have already been given?

i simply become too tired to endlessly repeat the same answers. but it seems there are usually others with more energy.

5. Mar 7, 2005

### HallsofIvy

Staff Emeritus
Take a disk and a washer and look at them! The washer has a hole in the middle that the disk doesn't have! That's when you use the washer method- when the area rotated around the axis does not extend all the way to the axis so you will have a hole in the center of the solid.
Actually, "washer" and "disk" are basically the same method: any problem that you use the "washer" on, you could do as two "disks"- Do the "outer" disk ignoring the missing part- taking the area right up to the axis, then do the same thing finding the volume of the missing inner portion and subtract.

6. Mar 8, 2005

### mathwonk

all volumes are computed by constructing a moving volume function, which at any stage cuts out an area. the area is the derivative of the volume function, and so the problem is easier dependening on how easy the area fucntion is. you can sweep out volumes by moving slices in any direction, upward or outward, or around a circle, or other ways. expanding a cylinder gives the shell metjhod, raising a plane along a line gives the "disc" method (assuming your volume was sewept out by a revilution), etc etc etc... i recommend you search for my earlier more detailed explanations, or simply read about cavalieri;s method.