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Homework Help: Wording question

  1. Jan 30, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider the solid S described below.
    The base of S is the region enclosed by the parabola y = 5 - 2x2 and the x-axis. Cross-sections perpendicular to the y-axis are squares.
    Find the volume V of this solid.

    2. Relevant equations

    3. The attempt at a solution
    I know how to answer these types of questions, but my question is what exactly does the question ask for? I can find the area bound by the parabola and the x-axis, but what does "cross-sections perpendicular to the y-axis are squares" mean?
    thanks for any help
  2. jcsd
  3. Jan 30, 2008 #2


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    If the bounding functions were, for example, [itex]y=x+1[/itex], [itex]y=-x+1[/itex] and [tex]y=0[/itex] then the solid would be a square pyramid.

    The object that's being described is something like a sqare 'bubble pyramid'.
  4. Jan 30, 2008 #3


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    Imagine squares made of foam. at the base of the parabola, since y= 5- 2x2 has x-intercepts at [itex]\pm\sqrt{5/2}[/itex] your square have height as well as base of length [itex]2\sqrt{5/2}[/itex] (and so area 10). As y increases the corresponding x values decrease and so does the height of the square. Your solid is bounded by 4 curved sides. Of course, there is the base which is that parabola itself. There will also be two "edges" arcing from (-1, 0, [itex]-\sqrt{5/2}[/itex]) down to (0, 5, 0) and from (1, 0, [itex]\sqrt{5/2}[itex]) down to (0, 5, 0).
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