1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook