Final answer:
By calculating the combined area of the floor and roof of the cinema hall and equating it to the area of the four walls, we can isolate and solve for the hall's height. The calculated height is approximately 8.9 m, which corresponds to option A. Therefore, the closest answer to the calculated height is 8.9 m, which corresponds to option A.
Step-by-step explanation:
To find the height of the hall, first calculate the area of the floor and the flat roof of the cinema hall. The area of a rectangle is found by multiplying the length by the width. Since both the floor and the roof have the same dimensions of 20 m length and 16 m breadth, their combined area is:
Area of floor and roof = 2 × (Length × Breadth)
= 2 × (20 m × 16 m)
= 2 × 320 m²
= 640 m²
The area of the four walls is equal to twice the combined area of the floor and the roof. Therefore, the area of the four walls is 640 m². The formula for the area of the walls is:
Area of walls = 2 × (Length + Breadth) × Height
640 m² = 2 × (20 m + 16 m) × Height
640 m² = 2 × 36 m × Height
640 m² = 72 m × Height
Dividing both sides by 72 m gives us the height:
Height = 640 m² / 72 m
Height = 8.89 m, approximately
Therefore, the closest answer to the calculated height is 8.9 m, which corresponds to option A.