The dimensions of a Cinema Hall are 100m, 60m and 15m. How many persons can sit in the hall, if each requires `150m^(3)` of air?

Answer

To solve the problem, we need to follow these steps:

### Step 1: Calculate the Volume of the Cinema Hall
The volume of a rectangular solid (like the cinema hall) can be calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]

Given dimensions:
- Length = 100 m
- Breadth = 60 m
- Height = 15 m

Now, substituting the values into the formula:
\[ \text{Volume} = 100 \, m \times 60 \, m \times 15 \, m \]

### Step 2: Perform the Multiplication
Now, we calculate:
\[ \text{Volume} = 100 \times 60 = 6000 \]
Then multiply by the height:
\[ 6000 \times 15 = 90000 \, m^3 \]

So, the volume of the cinema hall is:
\[ \text{Volume} = 90000 \, m^3 \]

### Step 3: Determine the Number of Persons that can be Accommodated
Each person requires 150 m³ of air. To find the number of persons that can fit in the cinema hall, we divide the total volume of the hall by the volume required per person:
\[ \text{Number of persons} = \frac{\text{Volume of cinema hall}}{\text{Volume required per person}} \]

Substituting the known values:
\[ \text{Number of persons} = \frac{90000 \, m^3}{150 \, m^3} \]

### Step 4: Perform the Division
Now, we calculate:
\[ \text{Number of persons} = 90000 \div 150 \]

Calculating this gives:
\[ 90000 \div 150 = 600 \]

### Conclusion
Thus, the number of persons that can sit in the cinema hall is:
\[ \text{Number of persons} = 600 \]

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