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Math Help - Volume help please!

  1. #1
    HMV
    HMV is offline
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    Volume help please!

    Find the volume generated by rotating the given region over x=1.
    http://i344.photobucket.com/albums/p335/HMV99/graph.jpg
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  2. #2
    MHF Contributor
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    using washers w/r to y ...

    V = \pi \int_0^1 1^2 - (1-y)^2 \, dy


    using cylindrical shells w/r to x ...

    V = 2\pi \int_0^1 (1-x)(1-x) \, dx


    or w/o calculus ...

    volume of cylinder - volume of cone

    \pi r^2 h - \frac{\pi}{3} r^2 h = \frac{2\pi}{3} r^2 h

    r = 1, h = 1
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