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Math Help - Need help with finding a volume of revolution with Cylindrical Shells method

  1. #1
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    Need help with finding a volume of revolution with Cylindrical Shells method

    y=2-0.5x, y=0, x=1, x=2, rotate about the x axis.
    I know that it will be easier to solve it with the regular method, but I need it with cylindrical shell.
    I cannot find the radius and the height.
    The final answer is 19pi/12
    Thanx
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    Re: Need help with finding a volume of revolution with Cylindrical Shells method

    Quote Originally Posted by shaharg View Post
    y=2-0.5x, y=0, x=1, x=2, rotate about the x axis.
    I know that it will be easier to solve it with the regular method, but I need it with cylindrical shell.
    I cannot find the radius and the height.
    If you must use the shell method, you will need to set up two integrals: one for 0\leq y\leq 1, in which the height of each shell is simply 1, and then another for \textstyle1\leq y\leq\frac32, in which the height of each shell is (4-2y)-1.
    Last edited by Reckoner; July 11th 2012 at 02:15 PM.
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    Re: Need help with finding a volume of revolution with Cylindrical Shells method

    Quote Originally Posted by Reckoner View Post
    If you must use the shell method, you will need to set up two integrals: one for 0\leq y\leq 1, in which the height of each shell is simply 1, and then another for \textstyle1\leq y\leq\frac32, in which the height of each shell is (4-2y)-1.
    So, what is the radius and what is the height?
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    MHF Contributor Reckoner's Avatar
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    Re: Need help with finding a volume of revolution with Cylindrical Shells method

    Quote Originally Posted by shaharg View Post
    So, what is the radius and what is the height?
    I suggest drawing a picture. The average radius of each shell is the distance from the axis of rotation to each given y-value. Since the axis of rotation is simply the x-axis, this distance is given by y. The "height" of each shell (horizontal distance from side to side) I have explained in my previous post. It should be clear from looking at a picture.
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    Re: Need help with finding a volume of revolution with Cylindrical Shells method

    Thank You
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