Mathematics
A room 5 m long, 4.5 m wide and 3.6 m high has one door 1.5 m by 2.4 m and two windows, each 1 m by 0.75 m. Find :
(i) the area of its walls, excluding doors and windows.
(ii) the cost of distempering its walls at the rate of ₹ 4.50 per m2.
(iii) the cost of painting its roof at the rate of ₹ 9 per m2.
Surface Area, Volume, Capacity
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Answer
(i) Given:
Dimensions of the room are 5 m long, 4.5 m wide and 3.6 m high.
Dimensions of the door are 1.5 m by 2.4 m.
Dimensions of the windows are 1 m by 0.75 m.
Remaining area = Total surface area of room - (Area of door + Area of window)
Total surface area of room = 2(l + b)h
= 2(5 + 4.5)3.6 m2
= 2 x 9.5 x 3.6 m2
= 68.4 m2
Area of door = l x b
= 1.5 x 2.4 m2
= 3.6 m2
Area of window = l x b
Area of two window = 2 x l x b
= 2 x 1 x 0.75 m2
= 1.5 m2
Remaining area = 68.4 - (3.6 + 1.5) m2
= 68.4 - 5.1 m2
= 63.3 m2
Hence, the area of room's walls, excluding doors and windows is 63.3 m2.
(ii) The rate of distempering = ₹ 4.50 per m2
Total cost = Area of wall x rate of distempering
= ₹ 63.3 x 4.50
= ₹ 284.85
Hence, the cost of distempering the walls of the room is ₹ 284.85.
(iii) The rate of painting = ₹ 9 per m2.
Area of roof = l x b
= 5 x 4.5 m2
= 22.5 m2
Total cost = Area of roof x Rate of painting
= ₹ 22.5 x 9
= ₹ 202.5
Hence, the cost of painting the roof of the room is ₹ 202.5.
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