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Math Help - Finding Volume by Washer/Disk/Cylindrical Shell

  1. #1
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    Finding Volume by Washer/Disk/Cylindrical Shell

    When finding the volume by either the washer, disk, or cylindrical shell, how would the limit be found?
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  2. #2
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    Quote Originally Posted by _rawr View Post
    When finding the volume by either the washer, disk, or cylindrical shell, how would the limit be found?

    Give me an example of the question you are doing and l can show you.
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  3. #3
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    Quote Originally Posted by nyasha View Post
    Give me an example of the question you are doing and l can show you.
    Find the volume of the solid that results when the shaded region is revolved around the x-axis.

    y=x; y=2- x^2

    [When graphed, the shaded region is about the y=x line.]
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  4. #4
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    Quote Originally Posted by _rawr View Post
    Find the volume of the solid that results when the shaded region is revolved around the x-axis.

    y=x; y=2- x^2

    [When graphed, the shaded region is about the y=x line.]




    Find the intersections points of these two functions and those are your limits depending on whether you are using horizontal strips of vertical strips.


    Note: The points of intersection are shown on the graph l uploaded. If using horizontal strips then take the y-values and if using the vertical strips then take the x-values.
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  5. #5
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    I see. Thank you very much for your help.
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  6. #6
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    how to solve integral of similar plot

    i have this problem: find the volume of solid bounded by 2x+y=6 and y=4x^2 rotated about the x-axis using cylindrical shells... the book's answer is 250pi/3. but i can't seem to get that answer.

    the plot is similar to that, and what i did is to separate the integrals into 2. one is the integral of 2*pi*y*(sqrt of y) from 0 to 4 and the second integral is the difference of the 2 functions. am i doing it right?
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  7. #7
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    Quote Originally Posted by ru_bled View Post
    i have this problem: find the volume of solid bounded by 2x+y=6 and y=4x^2 rotated about the x-axis using cylindrical shells... the book's answer is 250pi/3. but i can't seem to get that answer.

    the plot is similar to that, and what i did is to separate the integrals into 2. one is the integral of 2*pi*y*(sqrt of y) from 0 to 4 and the second integral is the difference of the 2 functions. am i doing it right?
    Are you using horizontal or vertical strips ?
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  8. #8
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    horizontal strips since i need to do it using cylindrical shells
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