Question

The dimensions of a hall are 40m, 25m and 20m. If each person requires 200 cubic meters, then the number of persons who can be accommodated in the hall are ?
A) 120
B) 150
C) 140
D) 100

Answer 1

Hint:
Here, in this question we have to find out the total number of people that can be accommodated in a hall. So, to find the total number of people that can be accommodated in a hall, firstly we have to find out the total volume of the hall. Then dividing this total volume of the hall with the volume required for each person will give us the number of people that can be accommodated in the hall.

Complete step by step solution:
The dimensions of the hall are length 40m, breadth 25m and height 20m.
Now, calculating the total volume of the hall\[{\rm{ = length \times breadth \times height}}\]
Therefore, total volume of the hall \[{\rm{ = 40}} \times {\rm{25}} \times 20{\rm{ = 20000}}{{\rm{m}}^3}\]
Now, we have to divide this total volume of the hall with the volume required for each person to get the total number of people that can be accommodated in the hall.
Volume requires for each person is given as \[200{{\rm{m}}^3}\]
Total number of person that can be accommodated in the hall\[ = \dfrac{{{\text{total volume of the hall}}}}{{{\text{volume requires for each person}}}}\]
Therefore, total number of person that can be accommodated in the hall \[{\rm{ = }}\dfrac{{20000}}{{200}} = 100\]

Hence, 100 persons can be accommodated in a hall of length 40m, breadth 25m and height 20m.
So, option D is correct.

Note:
Surface area is the sum of all the areas of the faces of an object or shape and Surface area is generally measured in square units. Volume is the amount of space occupied by an object in three-dimensional space. Volume is generally measured in cubic units.
Surface area of the cuboid\[{\rm{ = 2 \times [(L \times B) + (B \times H) + (L \times H)]}}\] where, L is the length, B is the breadth, H is the height of the cuboid.
Volume of the cuboid\[{\rm{ = L}} \times {\rm{B}} \times {\rm{H}}\] where, L is the length, B is the breadth, H is the height of the cuboid.