Question

375 persons can be accommodated in a room whose dimensions are in the ratio of  6 : 4 : 1. Calculate the area of the four walls of the room if the each person consumes 64m³ of air.

Answer 1

Given that:
No of persons accommodated in a room = 375
Ratio of dimensions of room = 6 : 4 : 1
∴ Length (l) of the room = 6x m
Breadth (b) of the room = 4x m
Height (h) of the room = x m
Air consumed by 1 person = 64m³
∴ Air consumed by 375 persons = 64 x 375
= 24,000m³
i.e., Volume of air in the room = 24,000m³ ..............................(1)
Also,
Volume (V) of the room is given by:-
V = l x b x h
Substituting (1) we get,
l x b x h = 24000
6x x 4x x x = 24,000
24 x 3 = 24,000

x3 = `(24000)/(24)`
x = `root(3)(1000)`
x = 10m
∴ Length (l) of the room = 6 x 10 = 60m
Breadth (b) of the room = 4 x 10 = 40m
Height (h) of the room = 1 x 10 = 10m
Now,
L.S.A of the room
= 2 x h x (l + b)
= 2 x 10 x (60 + 40)
= 20 x 100
= 2000m²
i.e., Area of the 4 walls of the room = 2000m².