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Math Help - Volumes of Revolution Question (Washer Method)

  1. #1
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    Volumes of Revolution Question (Washer Method)

    Use the washer method to find the volume of the solid generated by revolving the region bound by the lines and curves about the y-axis.

    The semicircle x = sqrt(25 - y^2) and the line x = 4.

    Thank you very much for your help!
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  2. #2
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    Quote Originally Posted by torrential View Post
    Use the washer method to find the volume of the solid generated by revolving the region bound by the lines and curves about the y-axis.

    The semicircle x = sqrt(25 - y^2) and the line x = 4.

    Thank you very much for your help!
    hi torrential,

    The washer radii are 4 and \sqrt{25-y^2}

    When y=0, x=\sqrt{25}=5

    Therefore the inner washer radii are 4.

    The curve intersects the line when 4=\sqrt{25-y^2}

    4=\sqrt{16},\ y^2=9,\ y=\pm3

    The surface area of inner disc is subtracted from the surface area of outer disc, to find the surface area of a washer.
    We use x as the radius since x=0 is the axis of revolution.

    Integrating these surfaces from y=-3 to 3 finds the vor.

    The surface of a disc is {\pi}r^2
    Attached Thumbnails Attached Thumbnails Volumes of Revolution Question (Washer Method)-vor-semicircle-line.jpg  
    Last edited by Archie Meade; February 15th 2010 at 06:27 PM.
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    Thank you very much! Your response really helped me!
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  4. #4
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    Cool!

    So, you need to calculate

    \int_{-3}^3\left({\pi}(25-y^2)-(\pi)4^2\right)dy
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