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Cross sections

  1. Jan 20, 2004 #1
    If the area enclosed by an ellipse 4x^2+y^2=1 and its cross section is perpendicular to the x-axis then its volume is?

    I dont have the slightest clue how to do this?

    Maybe solve for 2y^2=1-4x^2 set the integral equal to pi times the intergral of 1/4 to 1 of 1-4x^2?
  2. jcsd
  3. Jan 20, 2004 #2


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    It sounds to me like you're missing part of the problem...
  4. Jan 20, 2004 #3
    My calculus is rusty but here's the first idea which comes to mind. Solve for y:

    y = sqrt(1-4x^2)

    Then do an integral with limits 0 to 1/4, and multiply the total by 4. In other words (using a clunky capital S as an integral sign), solve this:

    4 [ S(0-.25) sqrt(1-4x^2) dx ]

    And that should be the answer. You may have trouble solving such a weird integral, but give it a go and see if the answer is reasonable.

  5. Jan 20, 2004 #4
    How can a planar fig occupy a volume I agree with Hurkyl u are missing something it must be rotated about some axis to have a solid figure
  6. Jan 26, 2004 #5
    In retrospect you're probably right (I wrote that response in a hurry). At the time I posted, I assumed he meant "area" since he provided insufficient information to solve a volume-related problem.

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