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Math Help - Volume Around y=r With Shells

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    Question Volume Around y=r With Shells

    The region R enclosed by the curves and is rotated about the line y=7. Use cylindrical shells to find the volume of the resulting solid.
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    Quote Originally Posted by shannon1111 View Post
    The region R enclosed by the curves and is rotated about the line y=7. Use cylindrical shells to find the volume of the resulting solid.
    x = 4y-29

    x = (y-8)^2 + 3

    4y-29 = (y-8)^2 + 3

    0 = y^2 - 20y + 96

    0 = (y - 8)(y - 12)

    y = 8 ... y = 12


    V = 2\pi \int_8^{12} (y-7)[(4y-29) - ((y-8)^2 + 3)] \, dy
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