Volume calculation

  • Thread starter Miike012
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  • #1
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Problem:

Find the volume of the solid:

y = 2 - x/2 bounded by y = 0, x = 1, x = 2.

Answer: 19pi/12.... I already know how to get the answer but....

what if wanted to use horizontal rec? For instance If I am using the vertical rec... the radius would be y = 2 - x/2... but if I use the horizontal rec would the radius be x = 2(2 - y) ? I tryed this value and integrated from y = 0 to y = 3/2... but did not get the correct answer....

Is it not possible to get the correct answer using horiz. rec?
 

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  • #2
SammyS
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Problem:

Find the volume of the solid:

y = 2 - x/2 bounded by y = 0, x = 1, x = 2.

Answer: 19pi/12.... I already know how to get the answer but....

what if wanted to use horizontal rec? For instance If I am using the vertical rec... the radius would be y = 2 - x/2... but if I use the horizontal rec would the radius be x = 2(2 - y) ? I tryed this value and integrated from y = 0 to y = 3/2... but did not get the correct answer....

Is it not possible to get the correct answer using horiz. rec?

Are you rotating this trapezoid around the x-axis to form the solid of revolution?

If so, then integrating w.r.t x is the disk method.

Integrating w.r.t. y is the shell method (cylindrical shells), so the radius is y itself. You will have to break the integration up into sum of two integrals.
 
  • #3
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Yes I am rotating across the x-axis. So is it possible to use horizontal rec?
 
Last edited:
  • #4
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Where can I learn about the shell and disk method? My teacher didnt mention these techniques.
 

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