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Volume of a solid with equilateral triangle cross-sections

  1. Apr 19, 2012 #1
    The base of a solid is the region bounded by the parabola x2 = 8y and the line y = 4 and each plane section perpendicular to the y-axis is an equilateral triangle. What is the volume of the solid?(Barron's Problem)

    so I solved for x since y must be used because the cross section is perpendicular to the y-axis. x=(8y)1/2. The area equation for an equilateral triangle is A = s2√(3)/4
    So I figured the volume of the cross section would be equal to the integral from 0 to 4 of (8y√(3))/4 which gives me 16√(3) which is apparently wrong. The answer is supposed to be 64√(3). I don't know what I did wrong.
     
    Last edited: Apr 19, 2012
  2. jcsd
  3. Apr 19, 2012 #2

    HallsofIvy

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    82= 64, not 8!
     
  4. Apr 19, 2012 #3
    I wrote down solving for x incorrectly its supposed to be √(8y) which allows my confusion to continue.
     
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