A room is 13 ft. It needs to be painted. The ceiling is 8 ft above the floor. there are two windows int he room, each one is 3 ft by 4 ft. The door is 2.5 ft by 6.5 ft. What is the area of the wall and ceiling? 1 gallon of paint covers 64.37sq ft. How many gallons are needed to paint the room? At $23.48 a gallon, what is the cost to paint the room?
You only provide one linear floor and ceiling dimension, 13 ft. Unless the room is square, you need to know two: length and width.
Why do you say "wall" and not "walls" ?
To find the area of the walls and ceiling, we need to calculate each separately.
First, let's start with the walls. Since we have a rectangular room with a height of 8 ft and a length of 13 ft, the total wall area is given by the formula:
Total Wall Area = (Perimeter of the room) × height of the room
To calculate the perimeter of the room, we only consider the length and width of the rectangular room (not the windows or door). The perimeter is given by the formula:
Perimeter of the room = 2 × (length of the room + width of the room)
In this case, the length of the room is 13 ft, and the width is unknown. However, the width can be calculated by subtracting the combined width of the two windows and the door from the total length of the room:
Width of the room = Total Length of the room - (Combined width of the windows + width of the door)
The combined width of the windows is 2 × (3 ft) = 6 ft, and the width of the door is 2.5 ft. Therefore, the width of the room would be:
Width of the room = 13 ft - (6 ft + 2.5 ft) = 4.5 ft
Now that we have the width and height of the room, we can calculate the perimeter and then the total wall area.
Perimeter of the room = 2 × (13 ft + 4.5 ft) = 2 × 17.5 ft = 35 ft
Total Wall Area = 35 ft × 8 ft = 280 sq ft
Next, let's calculate the area of the ceiling, which is a rectangle with its own length and width. The total area is given by the formula:
Area of the Ceiling = Length of the room × Width of the room
In this case, the length of the room is 13 ft, and the width of the room is 4.5 ft. Therefore:
Area of the Ceiling = 13 ft × 4.5 ft = 58.5 sq ft
Now, to find the total area to be painted, we sum up the wall area and the ceiling area:
Total Area to be Painted = Wall Area + Ceiling Area
Total Area to be Painted = 280 sq ft + 58.5 sq ft = 338.5 sq ft
Now, since 1 gallon of paint covers 64.37 sq ft, we can calculate the number of gallons needed as follows:
Number of gallons needed = Total Area to be Painted / Coverage per gallon
Number of gallons needed = 338.5 sq ft / 64.37 sq ft = 5.26 gallons (rounded up to the nearest gallon)
Finally, to calculate the cost of painting the room, we multiply the number of gallons needed by the cost per gallon:
Cost to paint room = Number of gallons needed × Cost per gallon
Cost to paint room = 5.26 gallons × $23.48/gallon = $123.39