What is the maximum diameter of a sphere that can pass through guard openings located at a height of 36" to 42"?

The maximum diameter of a sphere that can pass through guard openings located at a height of 36" to 42" is determined by considering how the sphere interacts with the dimensions of the openings. When estimating the maximum size of a sphere that can navigate through an opening at specified heights, one must visualize the sphere's ability to maneuver through that space without being obstructed.

In this scenario, the critical factor is the vertical distance between the two heights of 36" and 42". This creates a range of openings that can be treated as rectangular in nature when viewed from the top. The maximum diameter that can fit through is directly related to the width of that rectangular passage at the widest point, which in this case is the span from 36" to 42", effectively creating a slot that is 6" high.

When it comes to the diameter of the sphere, we can apply geometric principles about how the sphere would fit through such an opening. Calculating the maximum diameter, while keeping in mind that it has to fit horizontally and also cannot exceed the height of the opening, yields the maximum dimension.

Thus, the maximum diameter that can be calculated and still allow the sphere to pass through both points of the guard openings is 4-3