Final answer:
The volume of the hall is found by setting up an equation based on the area of the floor/ceiling and walls, then solving for the height and using it to calculate the volume. The correct volume is 1200 m³.
option d is the correct
Step-by-step explanation:
To find the volume of the hall, we must first establish the relationship between the areas of the floor/ceiling and the walls. According to the problem, the sum of the areas of the floor and ceiling equals the sum of the areas of the four walls.
Let h be the height of the hall.
The area of the floor and the ceiling combined is 2 × (length × breadth) = 2 × (15m × 12m) = 360 m².
The combined area of the four walls is 2 × (length + breadth) × height = 2 × (15m + 12m) × h = 54h m².
So we have 360 m² (floor + ceiling) = 54h m² (four walls).
To find the height (h), we can set up the equation 360 = 54h, solving for h gives us h = 360/54, which simplifies to h = 6.67m (approximately).
Once we have the height, we can calculate the volume of the hall using the formula for the volume of a rectangular prism: Volume = length × breadth × height.
Therefore, the volume is 15m × 12m × 6.67m = 1200 m³. This corresponds to option (d) 1200 m³.