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Thread: volume formed by rotating the region

  1. August 7th 2009, 07:28 AM #1
    dat1611
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    volume formed by rotating the region

    Find the volume formed by rotating the region enclosed by:
    x=9y and y^3=x with y>=0
    about the y-axis
    can anyone help with this
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  2. August 7th 2009, 07:53 AM #2
    Failure
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    Quote Originally Posted by dat1611 View Post
    Find the volume formed by rotating the region enclosed by:
    x=9y and y^3=x with y>=0
    about the y-axis
    can anyone help with this
    Well, the curves intersect at (-3,-27), (0,0) and (3,27) therefore:

    By the method of rings you get

    V=\int\limits_0^3\pi \left[(9y)^2-(y^3)^2\right]\, dy

    By the method of cylinders you get

    V=\int\limits_0^{27}2\pi x(x^{1/3}-\tfrac{1}{9}x)\,dx

    Hopefully they are the same ( V\approx 1308.69774).
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