<p>So, I am self studying calculus, and ran across a problem that i have no idea how to solve.

This is barron's AP calculus, 9th Edition, Chapter 7 : Applications of Integration to Geometry, Problem # 26.</p>

<p>The base of a solid is the region bounded by the parabola x^2 = 8y, and the line y = 4, and each plane section perpendicular to the y axis is an equilateral triangle. The volume of the solid is _____</p>

<p>The book says that the answer is 64 rad(3), but i have no idea how it got there.</p>

<p>I understand that i have to integrate the area * dx then multiply it by 2. But i have no idea how to get the area.</p>

<p>Can any one help me with this?? Thank you! (Please show full work)</p>