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Volume of a solid with known cross sections

  1. Apr 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Any cross sectional slice of a certain solid in a plane perpendicular to the x-axis is a square with side AB, with A lying on the curve [tex]y^2 = 4x[/tex] and B on the curve [tex]x^2 = 4y[/tex]. Find the volume of the solid lying between the points of intersection of these two curves.

    2. Relevant equations
    [tex]\int ^{b}_{a} A(x)dx[/tex]

    3. The attempt at a solution
    I'm not sure if I'm going in the right direction, but so far I've put the curves in terms of y, leaving me with [tex]y = 2\sqrt{x}[/tex] and [tex]y = \frac{x^2}{4}[/tex]. After graphing, I also know that the limits of integration will be from 0 to 4 since the points of intersection are at (0, 0) and (4, 4). From here on, I'm completely lost.

    Thanks :)
     
  2. jcsd
  3. Apr 14, 2009 #2
    The area of a square is s^2 where s is the length of one side. So, what is the length of one side? The distance from A to B, so find that from your graph (at an arbitrary x value and the expression should be in terms of y.)
     
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