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

1. Apr 19, 2012

Phyzwizz

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. Apr 19, 2012

HallsofIvy

82= 64, not 8!

3. Apr 19, 2012

Phyzwizz

I wrote down solving for x incorrectly its supposed to be √(8y) which allows my confusion to continue.