The base of a solid is the region bounded by the parabola x(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}= 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 = s^{2}√(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.

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# Homework Help: Volume of a solid with equilateral triangle cross-sections

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