Volume of a sold

  1. 1. The problem statement, all variables and given/known data
    The base of S is an elliptical region with boundary curve 9x^2 + 4y^2 = 36. Cross-sections perpindicular to the x-axis are isosceles right triangles with hypotenuse in the base.

    Find the volume of the described solid.

    2. Relevant equations
    V = {int} 1/2 b*h dy

    3. The attempt at a solution
    I found that I would have to use the symmetry to solve this. The only things I have are x^2 + y^2 = 1/2 and y = sqrt(.5 - x^2)

    Now i know I have to integrate an isosceles triangles area which is 1/2 b*h but I'm not sure what the base or the height will be.
  2. jcsd
  3. tiny-tim

    tiny-tim 26,016
    Science Advisor
    Homework Helper

    Hi vigintitres! :smile:
    Where do you get x^2 + y^2 = 1/2 from? :confused:

    9x^2 + 4y^2 = 36.
    The base is 2y.

    The height you can work out because it's a right-angled isoceles triangle. :wink:
  4. Find volume via method of cross-sections.
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