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

**shaikshavali** 11 Dec 2015, 07:59

### 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

**Murray** 12 Dec 2015, 05:22

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 water pipe).

You need to use different integration formulas for disks, washers and shells methods.

See this page for explanation and examples of disk and washer methods:

Volume of Solid of Revolution (Disk and Washer Methods)

And see this page for examples of Shell Method:

Shell Method: Volume of Solid of Revolution

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 water pipe).
You need to use different integration formulas for disks, washers and shells methods.
See this page for explanation and examples of disk and washer methods:
<a href="//www.intmath.com/applications-integration/4-volume-solid-revolution.php">Volume of Solid of Revolution (Disk and Washer Methods)</a>
And see this page for examples of Shell Method:
<a href="http://www.intmath.com/applications-integration/shell-method-volume-solid-revolution.php">Shell Method: Volume of Solid of Revolution</a>

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

**Merrano** 27 Feb 2024, 06:49

When we rotate a curve around the x (or y) axis, we can find its volume using the disc method, which works for any solid formed by revolution. If we make perpendicular cuts to the axis, it produces a series of discs, akin to those depicted in my watermelon example.

X

When we rotate a curve around the x (or y) axis, we can find its volume using the disc method, which works for any solid formed by revolution. If we make perpendicular cuts to the axis, it produces a series of discs, akin to those depicted in my watermelon example.

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