Question

How many people can be accommodated in a hall of length 16m, breadth \[12.5\]m and height \[4.5\]m. Assuming that \[3.6{{\rm{m}}^3}\] of air is required for each person?

Answer 1

Hint:
Here, we will find the total number of people that can be accommodated in a hall. We will first find out the total volume of the hall. Then dividing this total volume of the hall with the volume of air for each person we will get the number of people that can be accommodated in the hall.

Complete step by step solution:
The given dimensions of the hall are length 16m, breadth 12.5m and height 4.5m.
Now, we know that the hall has the shape of a cuboid.
So, the total volume of the hall\[ = {\rm{length}} \times {\rm{breadth}} \times {\rm{height}}\]
Substituting the values of length, breadth, and height in the formula, we get
Total volume of the hall \[ = 16 \times 12.5 \times 4.5 = 900{{\rm{m}}^3}\]
Now, we will divide this total volume of the hall by the volume of air for each person to get the total number of people that can be accommodated in the hall.
Volume of air for each person is given as \[3.6{{\rm{m}}^3}\].
Total number of person that can be accommodated in the hall \[ = \dfrac{{{\text{total volume of the hall}}}}{{{\text{volume of air for each person}}}}\]
Substituting the values in the formula, we get
Total number of person that can be accommodated in the hall \[{\rm{ = }}\dfrac{{900}}{{3.6}} = 250\]

Hence, 250 persons can be accommodated in a hall of length 16m, breadth 12.5m and height 4.5m.

Note:
Here, dimensions are given but the shape of the hall is not given. For calculating the volume we need to know the shape of the hall, for that analyzing the question becomes very important. As in the question, length, breadth, and height are given so the possible shape could be cuboid. That’s why we have used the formula of a cuboid to find the volume. Also, we need to divide the volume of the hall from the volume of air consumed by each person and not multiply them. Because multiplying the terms we will get the wrong answer.