Final answer:
The total cost of painting the walls and the ceiling of the cuboidal room is $2016, calculated by summing the areas of the walls and the ceiling and then multiplying by the cost per square meter of $24.
Step-by-step explanation:
To calculate the total cost of painting the walls and the ceiling of a cuboidal room, we first need to find the area that will be painted, and then multiply it by the cost per square meter. The room has a length of 6 meters, a width of 4 meters, and a height of 3 meters. We will not paint the floor, so we need to calculate the area of the four walls and the ceiling.
The area of the four walls is calculated as 2 times the height times the sum of the length and the width (since there are two walls of each dimension):
- Area of walls = 2 × height × (length + width) = 2 × 3 × (6 + 4) = 60 square meters.
The area of the ceiling is the length times the width:
- Area of ceiling = length × width = 6 × 4 = 24 square meters.
The total area to be painted is the sum of the area of the walls and the ceiling:
- Total area = Area of walls + Area of ceiling = 60 + 24 = 84 square meters.
Finally, we calculate the total cost by multiplying the total area by the cost per square meter:
- Total cost = Total area × Cost per square meter = 84 × $24 = $2016.
Therefore, the total cost of painting the walls and the ceiling of the room is $2016.