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

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

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>

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.