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Thread: 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.
    $\displaystyle x = 4y-29$

    $\displaystyle x = (y-8)^2 + 3$

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

    $\displaystyle 0 = y^2 - 20y + 96$

    $\displaystyle 0 = (y - 8)(y - 12)$

    $\displaystyle y = 8$ ... $\displaystyle y = 12$


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