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The Disk/Washer Method: Axis Of Revolution Question

  1. Aug 13, 2008 #1
    1. The problem statement, all variables and given/known data

    [​IMG]

    Find the volume of the solid generated by evolving the region bounded by y = sqrt(x), y = 0, x = 4, when revolved around the line x = 6

    2. Relevant equations

    The Disk/Washer Method -

    3. The attempt at a solution

    let R(y) = 6 - y^2
    r(y) = 2

    Okay. What I don't quite understand is why we translate the graph to the right 6 units, and letting the inner radius equal 2. Can anyone shed some light on why we do this? A counter-example would help me understand this easier.

    My $0.02... maybe you can clarify it:

    By translating the graph y = sqrt(x), 6 units to the left, the vertex point (0,0) now becomes (6,0)... and it's similar, as if, rotated by the y-axis. I know there is a gap of 2 units (from x = 4 and x = 6, as shown by the graph). But where does the subtraction come from?

    Carlo
     
  2. jcsd
  3. Aug 13, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    The gap of 2 is the distance from x=6 to x=4, which is 6-4. There's a subtraction in there too. Similarly the distance from x=y^2 to x=6 is 6-y^2. Subtracting a larger number from a smaller gives the distance between them.
     
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