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Math Help - Rotating circle

  1. #1
    Member Jones's Avatar
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    Rotating circle

    Hi, i need some help on this.

    a) Determine the volume dV of the cylindric(?) shell in the figure.

    the curve is y=16-x^2

    I took a picture of the image in the book, might help

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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Jones View Post
    Hi, i need some help on this.

    a) Determine the volume dV of the cylindric(?) shell in the figure.

    the curve is y=16-x^2

    I took a picture of the image in the book, might help

    ImageShack - Hosting :: picture022oj5.jpg
    <br />
dV=(2\ \pi\ x)\ y\ dx=(2\ \pi\ x)\ (16 - x^2)\ dx<br />

    RonL
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  3. #3
    Member Jones's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    <br />
dV=(2\ \pi\ x)\ y\ dx=(2\ \pi\ x)\ (16 - x^2)\ dx<br />

    RonL
    Hm, could you explain how you did that?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Jones View Post
    Hm, could you explain how you did that?
    The circumference of the shell is 2 \pi\ x the thickness is
    dx the height is y. To first order in dx the volume is:

    <br />
dV= (2 \pi x) y dx<br />

    If you want it more explicit its the difference in volume of the two cylinders of radius x
    and x+dx of heights y(x) and y(x+dx) or:

    <br />
dV= -\pi x^2 y(x) + \pi (x+dx)^2 y(x+dx)=\pi\ 2 \ x\ dx (16-x^2) +O(dx^2)<br />

    RonL
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