The base ofa solid is bounded by the parabola y = 1 – x² and the x-axis. Find the volume of the solid if the cross sections are equilateral triangles with bases perpendicular to the x-axis.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.