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Answer :
Final answer:
To protect a room of 40 feet by 65 feet with 10-foot-high joisted ceiling using specified heat detectors with a 50-foot listed spacing, only two heat detectors are needed, following the spacing guidelines.
Explanation:
The question involves determining the number of heat detectors required for a room with specified dimensions, while considering the listed spacing for the detectors and the orientation of the joists. To calculate the number of detectors, one must understand how the spacing guideline affects the layout of detectors in a space. Given the room's dimensions of 40 feet by 65 feet and a detector spacing of 50 feet, detectors will be placed in a grid pattern aligned with the room's dimensions.
First, determine how many rows of detectors are needed based on the room's shorter dimension (40 feet) and the detector's listed spacing (50 feet). In this case, only one row is needed since 40 feet is less than the maximum spacing of 50 feet. Next, calculate how many detectors are needed along the 65-foot length. Since 65 feet exceeds the 50-foot spacing, we'll need to space the detectors within this dimension according to the listed spacing. This results in needing at least two detectors along the 65-foot length.
Therefore, with one row across the width (40 feet) and two detectors along the length (65 feet), a total of two heat detectors will be required to protect the room.
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Rewritten by : Barada
Approximately 2 heat detectors are required for the room based on the specified 50-foot spacing and the room dimensions of 40 feet by 65 feet with a 10-foot-high joisted ceiling.
To determine the number of heat detectors required for the room, we need to calculate the area of the room and then determine the appropriate spacing based on the specifications provided.
1. Calculate the Area of the Room:
Given dimensions:
- Length = 65 feet
- Width = 40 feet
- Height (joisted ceiling) = 10 feet
Area = Length × Width = 65 feet × 40 feet = 2600 square feet
2. Determine the Coverage Area per Detector:
The heat detectors have a listed spacing of 50 feet. To find the coverage area per detector:
- The detectors cover a circular area with a radius equal to half of the listed spacing.
Radius of coverage = 50 feet / 2 = 25 feet
Coverage Area per detector = π × (25 feet)² ≈ 1963.5 square feet
3. Calculate the Number of Detectors Needed:
Divide the total area of the room by the coverage area per detector to find the number of detectors required:
Number of detectors = Area of the room / Coverage Area per detector
= 2600 square feet / 1963.5 square feet ≈ 1.32
Since the number of detectors must be a whole number, round up to the nearest whole number.
Number of detectors required = 2 detectors (since you cannot have partial detectors, you would round up)
Based on the calculations, approximately 2 heat detectors are required to adequately protect the room according to the specified spacing and coverage area per detector.
