IntMath Home » Forum home » Applications of Integration » Difference between disc method, washer method and shell meth

# Difference between disc method, washer method and shell meth [Solved!]

### My question

good morning mam, your interactive mathematics is very useful to me for clarify my doubt .Thank you

I have a small doubt:
what is the difference between DISC METHOD ,WASHER METHOD AND SHELL METHOD?

### Relevant page

4. Volume of Solid of Revolution by Integration

### What I've done so far

Tried to find it on IntMath, but couldnt

X

good morning mam, your interactive mathematics is  very useful to me for clarify my doubt .Thank you

I have a small doubt:
what is the difference between DISC METHOD ,WASHER METHOD AND SHELL METHOD?
Relevant page

<a href="/applications-integration/4-volume-solid-revolution.php">4. Volume of Solid of Revolution by Integration</a>

What I've done so far

Tried to find it on IntMath, but couldnt

## Re: Difference between disc method, washer method and shell meth

Hi Shaikshavali

The disc method for finding a volume of a solid of revolution is what we use if we rotate a single curve around the x- (or y-) axis. If we do that and take slices perpendicular to the axis, we will produce a series of discs (like my watermelon example on this page:)

4. Volume of Solid of Revolution by Integration

If we rotate an area between 2 curves, and then take slices, we won't have a discs, instead we'll have washers (like the ones given in the pictures at the top of the page above).

The Shell method approaches it from quite a different viewpoint. This time we end up with a set of hollow cylinders (something like a drinking glass). see this page:

Pauls Online Notes : Calculus I - Volumes of Solids of Revolution/Method of Cylinder

The integral that you use is not the same as the one used for disks or washers.

I will try to add Shell method to that page sometime soon.

X

Hi Shaikshavali

The disc method for finding a volume of a solid of revolution is what we use if we rotate a single curve around the x- (or y-) axis. If we do that and take slices perpendicular to the axis, we will produce a series of discs (like my watermelon example on this page:)

<a href="/applications-integration/4-volume-solid-revolution.php">4. Volume of Solid of Revolution by Integration</a>

If we rotate an area between 2 curves, and then take slices, we won't have a discs, instead we'll have washers (like the ones given in the pictures at the top of the page above).

The Shell method approaches it from quite a different viewpoint. This time we end up with a set of hollow cylinders (something like a drinking glass). see this page:

<a href="http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithCylinder.aspx">Pauls Online Notes : Calculus I - Volumes of Solids of Revolution/Method of Cylinder</a>

The integral that you use is not the same as the one used for disks or washers.

I will try to add Shell method to that page sometime soon.