Mathematics
The dining hall of a hotel is 75 m long, 60 m broad and 16 m high. It has five doors 4 m by 3 m each and four windows 3 m by 1.6 m each. Find the cost of :
(i) papering its walls at the rate of ₹ 12 per m2;
(ii) carpeting its floor at the rate of ₹ 25 per m2.
Surface Area, Volume, Capacity
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Answer
(i) Given:
Dimensions of the room are 75 m long, 60 m broad and 16 m high.
Dimensions of the door are 4 m by 3 m.
Dimensions of the windows are 3 m by 1.6 m.
Remaining area = Total surface area of room - (Area of door + Area of window)
Total surface area of room = 2(l + b)h
= 2(75 + 60)16 m2
= 2 x 135 x 16 m2
= 4,320 m2
Area of door = l x b
Area of 5 doors = 5 x l x b
= 5 x 4 x 3 m2
= 60 m2
Area of window = l x b
Area of four window = 4 x l x b
= 4 x 3 x 1.6 m2
= 19.2 m
Remaining area = 4,320 - (60 + 19.2) m2
= 4,320 - 79.2 m2
= 4,240.8 m2
The rate of papering = ₹ 12 per m2
Total cost = Area of wall x rate of papering
= ₹ 4,240.8 x 12
= ₹ 50,889.6
Hence, the cost of papering walls of dining hall is ₹ 50,889.6.
(ii) The rate of carpeting = ₹ 25 per m2.
Area of floor = l x b
= 75 x 60 m2
= 4500 m2
Total cost = Area of floor x Rate of carpeting
= ₹ 4500 x 25
= ₹ 112,500
Hence, the cost of carpeting the floor of dining hall is ₹ 112,500.
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