What is the maximum distance a heat detector can be from any point on a smooth ceiling given a listed spacing of 50′?

• A. 20 ft
• B. 28 ft
• C. 35 ft
• D. 40 ft

Answer: (C)

On a smooth ceiling, heat detectors spaced 50 ft apart are placed center-to-center in a grid. The farthest point from any detector will be at the center of the square formed by four detectors. The distance from that center to a corner detector is half the square’s diagonal. For a square with side 50 ft, the diagonal is 50√2 ft, so the center-to-detector distance is (50√2)/2 = 25√2 ft ≈ 35.4 ft. Rounding to the nearest foot gives about 35 ft.