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Thread: Volume

  1. #1
    Newbie leebatt's Avatar
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    Volume

    Consider the given curves to do the following. 8 y = x^3, y = 0 , x = 4 Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8.
    Last edited by leebatt; May 10th 2010 at 09:29 AM.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by leebatt View Post
    Consider the given curves to do the following. 8 y = x^3, y = 0 , x = 4 Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8.
    did you sketch a graph ?

     <br />
V = 2\pi \int_0^8 (8-y)(4 - 2\sqrt[3]{y}) \, dy<br />


    check the result by using washers ...

     <br />
V = \pi \int_0^4 8^2 - \left(8 - \frac{x^3}{8}\right)^2 \, dx<br />
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  3. #3
    Newbie leebatt's Avatar
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    I keep getting (1152 * Pi)/7. I am confused about why you have 4 - 2y^(1/3) when using the method of cylindrical shells. For the washer method
    it makes sense. The outer radius is 8 and the inner is 8 - x^3/8.

    I tried checking it with Maple and it still spits out the answer the answer from above. Maple just integrates Pi*(8-x^3/8)^2 over the interval x = 0 to x = 4.

    Thank you for your time
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  4. #4
    Newbie leebatt's Avatar
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    I see

    I see where my error is. It is bounded by x = 4.
    Thank you very much.
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