William has been contracted to paint a school classroom. The classroom is 20 m long, 15 m wide and 5 m high. There are four windows (2m by 3m) and a door (2m by 1m).
a) What is the cost of painting the ceiling at N$ 6.50 /m²? [5 marks]
b) What is the cost of painting the walls (excluding the windows and door) at N$ 8.50 /m²? [5 marks]
c) What is the cost of tiling the floor using tiles (20 cm by 20 cm) that are sold in boxes of 50 tiles each at N$ 50 per box? [5 marks]
d) What is the cost of providing air conditioning for this classroom at N$
2(20*5)+2(15*5)=350
350*8.50=2975
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1950
To find the cost of painting the ceiling, we need to calculate the area of the ceiling and multiply it by the cost per square meter.
a) The ceiling's area can be calculated by multiplying the length and width:
Area of ceiling = Length * Width
Area of ceiling = 20 m * 15 m
Area of ceiling = 300 m²
Cost of painting the ceiling = Area of ceiling * Cost per m²
Cost of painting the ceiling = 300 m² * N$ 6.50 /m²
Cost of painting the ceiling = N$ 1950
Therefore, the cost of painting the ceiling is N$ 1950.
b) To find the cost of painting the walls (excluding the windows and door), we need to calculate the wall area, excluding the windows and door, and multiply it by the cost per square meter.
Surface area of the walls = 2 * (Length * Height + Width * Height) - (Area of windows + Area of door)
Area of windows = Number of windows * Area of each window
Area of windows = 4 * (2 m * 3 m)
Area of windows = 24 m²
Area of door = Area of the door
Area of door = 2 m * 1 m
Area of door = 2 m²
Surface area of the walls = 2 * ((20 m * 5 m) + (15 m * 5 m)) - (24 m² + 2 m²)
Surface area of the walls = 2 * (100 m² + 75 m²) - (24 m² + 2 m²)
Surface area of the walls = 2 * (175 m²) - (26 m²)
Surface area of the walls = 350 m² - 26 m²
Surface area of the walls = 324 m²
Cost of painting the walls = Surface area of the walls * Cost per m²
Cost of painting the walls = 324 m² * N$ 8.50 /m²
Cost of painting the walls = N$ 2754
Therefore, the cost of painting the walls (excluding the windows and door) is N$ 2754.
c) To find the cost of tiling the floor, we need to calculate the area of the floor and divide it by the number of tiles per box. Then we multiply it by the cost per box.
Area of the floor = Length * Width
Area of the floor = 20 m * 15 m
Area of the floor = 300 m²
Number of tiles needed = Area of the floor / Area of each tile
Area of each tile = 20 cm * 20 cm = 0.2 m * 0.2 m = 0.04 m²
Number of tiles needed = 300 m² / 0.04 m²
Number of tiles needed = 7500 tiles
Number of boxes needed = Number of tiles needed / Tiles per box
Tiles per box = 50 tiles
Number of boxes needed = 7500 tiles / 50 tiles
Number of boxes needed = 150 boxes
Cost of tiling the floor = Number of boxes needed * Cost per box
Cost of tiling the floor = 150 boxes * N$ 50 per box
Cost of tiling the floor = N$ 7500
Therefore, the cost of tiling the floor is N$ 7500.
Note: The cost of providing air conditioning for the classroom was not specified in the question.