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Thread: Find Volume of Solid formed by revolving y=4−x^2, x-axis, y-axis about y=4

  1. #1

    Unhappy Find Volume of Solid formed by revolving y=4−x^2, x-axis, y-axis about y=4

    Here is the question:
    Find the volume of the solid obtained by rotating the region bounded by the curve y = 4 − x2, thex-axis and the y-axis about the line y = 4.





    I don't know how to use the shell method. I cannot figure out what the radius should be and what the height should be. I have no idea what to do.

  2. #2
    Elite Member
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    There is a whole chapter on this in your book. I hope you have not been sleeping in class. Anyway...

    Consider a Right Circular Cylinder. It's volume is given by: [tex]V = \pi r^{2}h[/tex]

    1) Find the Partial Derivative wrt r, holding h constant. [tex]dV = 2\pi r\cdot h\;dr[/tex] -- In the Differential Form
    This gives the basic setup for shells. Find those pieces. Associate the x and y axes with r and h and integrate along the "r"-axis. h will be perpendicular to r.

    2) Find the Partial Derivative wrt h, holding r constant. [tex]dV = \pi r^{2}\;dh[/tex] -- In the Differential Form
    This gives the basic setup for disks. Find those pieces. Associate the x and y axes with r and h and integrate along the "h"-axis. r will be perpendicular to h.

    Let's see your work. You must have SOMTHING to show us. Otherwise, we can only guess where you are struggling.

    BTW: Hang in there! Keep trying. You'll get it.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

  3. #3
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by ireallyneedhelpwithmath View Post
    Find the volume of the solid obtained by rotating the region bounded by the curve y = 4 − x2, the x-axis and the y-axis about the line y = 4.

    I don't know how to use the shell method. I cannot figure out what the radius should be and what the height should be. I have no idea what to do.
    Then the first thing to do is to learn about this method. While it is not reasonably feasible to attempt to provide you with classroom instruction within this environment, there are loads of great lessons available online, such as this (he calls the shells "cylinders", but it's the same thing), this, this, this, this, and this.

    Please study at least two lessons from the above links (or other sites). Then please review the assistance provided in the first reply you received, and then attempt the exercise. If you get stuck, you can then reply with a clear listing of your thoughts and efforts so far, at which point we can try to help you get un-stuck. Thank you!

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