If spacing between detectors is 9.1 meters, what is the maximum distance (in meters) a point on the ceiling may be from the nearest detector?

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Multiple Choice

If spacing between detectors is 9.1 meters, what is the maximum distance (in meters) a point on the ceiling may be from the nearest detector?

Explanation:
In a ceiling detector grid, the farthest point from any detector occurs at the center of a square formed by four neighboring detectors. The distance from that center to each of the four detectors is half of the square’s diagonal. So the maximum distance is spacing × sqrt(2) / 2, which is the same as spacing / sqrt(2). Plugging in 9.1 m gives 9.1 / sqrt(2) ≈ 9.1 / 1.414 ≈ 6.43 m. Among the given options, 6.37 m is the closest value, so that is the best choice. Minor differences can come from rounding sqrt(2) differently, but the concept and the approximate distance are clear.

In a ceiling detector grid, the farthest point from any detector occurs at the center of a square formed by four neighboring detectors. The distance from that center to each of the four detectors is half of the square’s diagonal. So the maximum distance is spacing × sqrt(2) / 2, which is the same as spacing / sqrt(2).

Plugging in 9.1 m gives 9.1 / sqrt(2) ≈ 9.1 / 1.414 ≈ 6.43 m. Among the given options, 6.37 m is the closest value, so that is the best choice. Minor differences can come from rounding sqrt(2) differently, but the concept and the approximate distance are clear.

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