A classroom is 10 m long, 6.4 m wide and 5m high. If each student be given `1.6 m^(2)` of the floor area, how many students can be accommodated in the room ? How many cubic metres of air would each student get ?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the area of the classroom floor.
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]

Given:
- Length = 10 m
- Width = 6.4 m

Calculating the area:
\[ \text{Area} = 10 \, \text{m} \times 6.4 \, \text{m} = 64 \, \text{m}^2 \]

### Step 2: Determine how many students can be accommodated.
Each student requires an area of:
\[ 1.6 \, \text{m}^2 \]

To find the number of students that can be accommodated, we divide the total area of the classroom by the area required per student:
\[ \text{Number of students} = \frac{\text{Total Area}}{\text{Area per student}} \]
\[ \text{Number of students} = \frac{64 \, \text{m}^2}{1.6 \, \text{m}^2} \]

Calculating:
\[ \text{Number of students} = 40 \]

### Step 3: Calculate the volume of the classroom.
The volume of a cuboid is given by the formula:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]

Given:
- Height = 5 m

Calculating the volume:
\[ \text{Volume} = 10 \, \text{m} \times 6.4 \, \text{m} \times 5 \, \text{m} \]
\[ \text{Volume} = 320 \, \text{m}^3 \]

### Step 4: Calculate the volume of air available per student.
To find out how much air each student gets, we divide the total volume of the classroom by the number of students:
\[ \text{Volume of air per student} = \frac{\text{Total Volume}}{\text{Number of students}} \]
\[ \text{Volume of air per student} = \frac{320 \, \text{m}^3}{40} \]

Calculating:
\[ \text{Volume of air per student} = 8 \, \text{m}^3 \]

### Final Answers:
- Number of students that can be accommodated: **40**
- Volume of air each student gets: **8 m³**

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