A school auditorium is 40m long, 30m broad and 12m high. If each student requires `1.2m^(2)` of the floor area, find the maximum number of students that can be accomodated in this auditorium. Also, find the volume of air available in the auditorium, for each student.

Answer

To solve the problem step by step, we will first calculate the area of the auditorium, then find the maximum number of students that can be accommodated, and finally calculate the volume of air available per student.

### Step 1: Calculate the Area of the Floor of the Auditorium

The area of the floor can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 40 m
- Breadth = 30 m

Substituting the values:
\[ \text{Area} = 40 \, \text{m} \times 30 \, \text{m} = 1200 \, \text{m}^2 \]

### Step 2: Calculate the Maximum Number of Students

Each student requires an area of \(1.2 \, \text{m}^2\). To find the maximum number of students that can be accommodated, we divide the total area by the area required per student:
\[ \text{Maximum Number of Students} = \frac{\text{Total Area}}{\text{Area per Student}} = \frac{1200 \, \text{m}^2}{1.2 \, \text{m}^2} \]

Calculating this gives:
\[ \text{Maximum Number of Students} = 1000 \]

### Step 3: Calculate the Volume of the Auditorium

The volume of the auditorium can be calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]
Given:
- Height = 12 m

Substituting the values:
\[ \text{Volume} = 40 \, \text{m} \times 30 \, \text{m} \times 12 \, \text{m} = 14400 \, \text{m}^3 \]

### Step 4: Calculate the Volume of Air Available per Student

To find the volume of air available for each student, we divide the total volume by the number of students:
\[ \text{Volume of Air per Student} = \frac{\text{Total Volume}}{\text{Number of Students}} = \frac{14400 \, \text{m}^3}{1000} \]

Calculating this gives:
\[ \text{Volume of Air per Student} = 14.4 \, \text{m}^3 \]

### Final Answers:
- Maximum number of students that can be accommodated: **1000**
- Volume of air available for each student: **14.4 m³**