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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.

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