Question

A class room is 7m long, 6m wide and 4m high. It has two doors each of 3m x 1.4m and six windows each of 2m x 1m. The interior walls are to be coloured at the rate of Rs.15per m². Find the cost of colouring the walls.

Answer 1

Given that:
Dimensions of the class room:
Length (l₁) of the room = 7m
Breadth (b₁) of the room = 6m
Height (h₁) of the room = 4m
Dimensions of the doors:
Length (l₂) = 3m
Breadth (b₂) = 1.4m
No. of doors = 2
Dimensions of the windows:
Length (l₃) = 2m
Breadth (b₃) = 1m
No. of windows = 6
Area of doors
= (l₂ x b₂) x 2
= (3 x 1.4) x 2
= 4.2 x 2
= 8.4m²
Area of windows
= (l₃ x b₃) x 6
= (2 x 1) x 6
= 2 x 6
= 12m²
Now,
T.S.A of the room
= 2 x {(l₁ x b₁) + (b₁ x h₁) + (h₁ x l₁)}
= 2 x {(7 x 6) + (6 x 4) + (4 x 7)}
= 2 x  {42 + 24 + 28}
= 2 x 94
= 188m²
Since the iner walls of the room has to be painted,
∴ Total area to be painted
= T.S.A of the room - (Ar . of doors) - (Ar . of windows)
= 188 - 8.4 - 12
= 179.6 - 12
= 167.6m²
Cost of colouring 1m² area = Rs. 15
∴ Cost of colouring 167.6m² area of the wall
= Rs.15 x 167.6
= Rs.2514.