Volume Calculation: Disk, Washer & Shell Methods

[jacy]

Hi,
Is there a guideline that one can follow when finding the volume of a solid obtained by revolving over a region. The three methods that i know are disk, washer, and shell method. But i don't know when to apply which method. My book doesn't explain it clearly. If anyone could help me with this, i will appreciate it. Thanking you, and have a safe and wonderful holiday.

 

[marlon]

Hi,
Is there a guideline that one can follow when finding the volume of a solid obtained by revolving over a region. The three methods that i know are disk, washer, and shell method. But i don't know when to apply which method. My book doesn't explain it clearly. If anyone could help me with this, i will appreciate it. Thanking you, and have a safe and wonderful holiday.

Depends on the symmetry of the object and how it is rotated, but you can apply both if you want. Actually, this is a good exercise...

Check out :

http://mathdemos.gcsu.edu/shellmethod/ I used this website when i tutored students in college. I recommend it...
disk and shell method

regards
marlon

 

[Tide]

You could use Pappus' Second Theorem.

 

[jacy]

Depends on the symmetry of the object and how it is rotated, but you can apply both if you want. Actually, this is a good exercise...
Check out :
http://mathdemos.gcsu.edu/shellmethod/ I used this website when i tutored students in college. I recommend it...
disk and shell method
regards
marlon

thanks marlon, i will check it out.

 

[jacy]

You could use Pappus' Second Theorem.

I am not familiar with Pappus' Second theorem. We never learned that theorem. Thanks

 

[kant]

Hi,
Is there a guideline that one can follow when finding the volume of a solid obtained by revolving over a region. The three methods that i know are disk, washer, and shell method. But i don't know when to apply which method. My book doesn't explain it clearly. If anyone could help me with this, i will appreciate it. Thanking you, and have a safe and wonderful holiday.

You use the disk method when you know you can distinquish a inner and outer fuction, and want to produce a glass china.
To use the waster method, you are trying to find many A(x), to do a intergral of many A(x)dx s. you see, A(x) can have different geometries( If you were to do a disk erercise with and waster method, then A(x) is always a damn circle)
The shell method is sort of like the waster method, but all you are doing is rotating a figure across a given axis.
My recommendation is to read that section 5 times, and try to understand it intuitively. My advice cannot do a damn thing for you, but it helps me to reflect more deeply.

 

[siddharth]

I am not familiar with Pappus' Second theorem. We never learned that theorem. Thanks

http://mathworld.wolfram.com/PappussCentroidTheorem.html"
The theorem is very interesting, is it not?

 

[jacy]

http://mathworld.wolfram.com/PappussCentroidTheorem.html"
The theorem is very interesting, is it not?

Thanks Siddharth, Tide, Marlon, and Kant. All u guys have a Happy New Year.