How many persons can be accommodated in a hall of length 16m, breadth 12.5 m and height 4.5 m, assuming that `3.6m^(3)` of air is required for each person?

Answer

To solve the problem of how many persons can be accommodated in a hall with given dimensions, we will follow these steps:

### Step 1: Identify the dimensions of the hall
- Length = 16 m
- Breadth = 12.5 m
- Height = 4.5 m

### Step 2: Calculate the volume of the hall
To find the volume of the hall, we use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]

Substituting the values:
\[ \text{Volume} = 16 \, \text{m} \times 12.5 \, \text{m} \times 4.5 \, \text{m} \]

### Step 3: Perform the multiplication
Calculating the volume step-by-step:
1. First, calculate \( 16 \times 12.5 \):
\[ 16 \times 12.5 = 200 \, \text{m}^2 \]
2. Now multiply the result by the height (4.5 m):
\[ 200 \, \text{m}^2 \times 4.5 \, \text{m} = 900 \, \text{m}^3 \]

Thus, the volume of the hall is \( 900 \, \text{m}^3 \).

### Step 4: Determine the air requirement per person
According to the problem, each person requires \( 3.6 \, \text{m}^3 \) of air.

### Step 5: Calculate the total number of persons that can be accommodated
To find the number of persons that can be accommodated, we divide the total volume of the hall by the volume of air required per person:
\[ \text{Number of persons} = \frac{\text{Total Volume}}{\text{Volume per person}} \]
\[ \text{Number of persons} = \frac{900 \, \text{m}^3}{3.6 \, \text{m}^3} \]

### Step 6: Perform the division
Calculating the number of persons:
\[ \text{Number of persons} = 250 \]

### Final Answer
Therefore, the total number of persons that can be accommodated in the hall is **250**.

---