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Math Help - Mth101 Questio No1

  1. #1
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    Mth101 Questio No1

    Use cylindrical shells to find the volume of the solid generated when the region is enclosed by the given curves is revolved about the x-axis.
    y^2=x, y=1, x=0
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    Quote Originally Posted by TAHIR View Post
    Use cylindrical shells to find the volume of the solid generated when the region is enclosed by the given curves is revolved about the x-axis.
    y^2=x, y=1, x=0
    The region looks like this:
    Attached Thumbnails Attached Thumbnails Mth101 Questio No1-bbb.gif  
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    Quote Originally Posted by TAHIR View Post
    Use cylindrical shells to find the volume of the solid generated when the region is enclosed by the given curves is revolved about the x-axis.
    y^2=x, y=1, x=0
    Why cylindrical shells? I think the washer method is better.
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  4. #4
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    Quote Originally Posted by TAHIR View Post
    Use cylindrical shells to find the volume of the solid generated when the region is enclosed by the given curves is revolved about the x-axis.
    y^2=x, y=1, x=0
    Hello,

    I've used curvature's diagram to show you where you can find those cylindrical shells: see attachment.

    One shell is calculated by:
    s=2 \pi y \cdot x Substitute x = y^2 into this equation and you'll get:
    s = 2 \pi y^3

    Now sum up all shells between the given bounds and you get the volume of the solid:

    V = \int_0^1 2 \pi y^3 dy = \left. \frac{1}{2} \pi y^4 \right|_0^1 = \frac{1}{2} \pi
    Attached Thumbnails Attached Thumbnails Mth101 Questio No1-cylindrical_shell.gif  
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