How many persons can be accommodated in a dining hall of dimensions `(20 m xx 15 m 4.5 m)`, assuming that each person requires `5 m^(3)` of air ?

Options

A. 250
B. 270
C. 320
D. 300

Answer

To solve the problem of how many persons can be accommodated in a dining hall with dimensions \(20 \, m \times 15 \, m \times 4.5 \, m\), where each person requires \(5 \, m^3\) of air, we will follow these steps:

### Step 1: Calculate the Volume of the Dining Hall
The volume \(V\) of a rectangular prism (which is the shape of the dining hall) can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Substituting the given dimensions:
\[ V = 20 \, m \times 15 \, m \times 4.5 \, m \]

### Step 2: Perform the Multiplication
Now, we will calculate the volume:
\[ V = 20 \times 15 = 300 \, m^2 \]
Next, we multiply this result by the height:
\[ V = 300 \, m^2 \times 4.5 \, m = 1350 \, m^3 \]

### Step 3: Calculate the Number of Persons
Each person requires \(5 \, m^3\) of air. To find the total number of persons \(N\) that can be accommodated, we can use the formula:
\[ N = \frac{\text{Total Volume}}{\text{Volume per person}} \]
Substituting the values we have:
\[ N = \frac{1350 \, m^3}{5 \, m^3} \]

### Step 4: Perform the Division
Now, we will perform the division:
\[ N = 270 \]

### Conclusion
Thus, the total number of persons that can be accommodated in the dining hall is \(270\).

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