1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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 by cross-section: ellipse and equilateral triangle cross sections?

  1. Feb 3, 2010 #1
    Volume by cross-section: ellipse and equilateral triangle cross sections??

    1. The problem statement, all variables and given/known data

    The base of a solid is the region bounded by the ellipse 4x^2+9y^2=36. Find the volume of the solid given that cross sections perpendicular to the x-axis are:
    a) equilateral triangles
    b) squares


    2. Relevant equations



    3. The attempt at a solution

    So I'm not really sure how ellipses work.. how can I sketch this ellipse?
    Beyond that.. I try to calculate the area of the triangle and then integrate in terms of y so the base is changing according to the ellipse curve.

    I write the ellipse as:

    y = +/-sqrt((-4/9)x^2 + 4)

    So the base of the triangle is 2(sqrt((-4/9)x^2 + 4))
    And has that as the length on all side since it is equilateral.
    Then I try to find the height using Pythagoras and get

    h = +/-sqrt((-4/3)x^2 + 12)

    Then now I have the area of the triangle as (1/2)bh, which is =

    A = (1/2)(2(sqrt((-4/9)x^2 + 4)))(sqrt((-4/3)x^2 + 12))

    Then I can integrate in terms of x.. does that look correct so far?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Volume by cross-section: ellipse and equilateral triangle cross sections?
Loading...