A solid region has a circular base of radius 3 whose cross-sections perpendicular to the base and parallel to the y-axis are equilateral triangles.
Placing the circular base in the plane so it’s centered at the origin, determine the side length of the cross-sectional triangle that passes through (x, 0), for −3 ≤ x ≤ 3. (Your final answer will depend on x.) Draw a clear diagram in your solution.