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?
b) What is the cost of painting the walls (excluding the windows and door) at N$ 8.50
/m²?
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?
d) What is the cost of providing air conditioning for this classroom at N$ 60 / m³?
20 m
Student
235
William is 450
To calculate the cost of painting the ceiling, we need to find the area of the ceiling first.
The area of a rectangle can be calculated by multiplying its length by its width.
The length of the classroom is 20 m and the width is 15 m, so the area of the ceiling is:
20 m * 15 m = 300 m²
Once we have the area, we can multiply it by the cost per square meter to find the total cost:
300 m² * N$ 6.50/m² = N$ 1,950
Therefore, the cost of painting the ceiling is N$ 1,950.
Now let's move on to calculating the cost of painting the walls. We need to exclude the area covered by the windows and door.
The total area of the walls can be found by multiplying the perimeter of the classroom by its height.
The perimeter of a rectangle can be calculated by adding the lengths of all its sides.
The length of the classroom is 20 m, the width is 15 m, and the height is 5 m. So the perimeter is:
2 * (20 m + 15 m) = 2 * 35 m = 70 m
Now we can calculate the area of the walls:
70 m * 5 m = 350 m²
To exclude the area covered by the windows and door, we need to subtract their areas from the total wall area.
The area of the windows is 4 windows * (2 m * 3 m) = 24 m²
The area of the door is 2 m * 1 m = 2 m²
So the final area of the walls to be painted is:
350 m² - 24 m² - 2 m² = 324 m²
Multiply this by the cost per square meter to find the total cost:
324 m² * N$ 8.50/m² = N$ 2,754
Therefore, the cost of painting the walls (excluding the windows and door) is N$ 2,754.
Moving on to tiling the floor, we need to find the total number of tiles needed.
The area of the floor can be calculated by multiplying its length by its width.
The length of the classroom is 20 m and the width is 15 m, so the area of the floor is:
20 m * 15 m = 300 m²
To find the number of tiles needed, we need to convert the area into the same unit as the tile size.
Since the tile size is given in centimeters, we need to convert square meters to square centimeters.
1 square meter = 10,000 square centimeters
So the area of the floor in square centimeters is:
300 m² * 10,000 cm²/m² = 3,000,000 cm²
Now we need to calculate how many tiles are needed.
The area of each tile is 20 cm * 20 cm = 400 cm²
Divide the total floor area by the area of each tile to find the number of tiles needed:
3,000,000 cm² / 400 cm² = 7,500 tiles
Since each box contains 50 tiles, we need to calculate the number of boxes needed:
7,500 tiles / 50 tiles per box = 150 boxes
Multiply the number of boxes by the cost per box to find the total cost:
150 boxes * N$ 50/box = N$ 7,500
Therefore, the cost of tiling the floor is N$ 7,500.
Finally, let's calculate the cost of providing air conditioning.
To find the volume of the classroom, we need to multiply its length, width, and height:
20 m * 15 m * 5 m = 1,500 m³
Multiply the volume by the cost per cubic meter to find the total cost:
1,500 m³ * N$ 60/m³ = N$ 90,000
Therefore, the cost of providing air conditioning for this classroom is N$ 90,000.