Advertisements
Advertisements
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.
Advertisements
Solution
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.
APPEARS IN
RELATED QUESTIONS
The floor of a rectangular hall has a perimeter 250 m. If the cost of panting the four walls at the rate of Rs.10 per m2 is Rs.15000, find the height of the hall.
[Hint: Area of the four walls = Lateral surface area.]
A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm in following figure. The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2. Find the total expenses required for polishing and painting the surface of the bookshelf.
The paint in a certain container is sufficient to paint on area equal to 9.375 m2. How manybricks of dimension 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 300 cm3 of a liquid?
If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that \[\frac{1}{V} = \frac{2}{S}\left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)\]
The breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu. dm. Find its dimensions.
The dimensions of a cinema hall are 100 m, 50 m and 18 m. How many persons can sit in the hall, if each person requires 150 m3 of air?
Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down in to a single cube whose diagonal is 12 `sqrt(3)` cm. Find the edges of three cubes.
The length and breadth of a cuboid are 20 cm and 15 cm respectively. If its volume is 2400 cm3, find its height.
The dimensions of a hall is 10 m × 9 m × 8 m. Find the cost of white washing the walls and ceiling at the rate of ₹ 8.50 per m2
