A room is 14 x 21 ft.It needs to be painted.The ceiling is eight above the floor.There are 2 windows in the room, each one is 3 ft by 4 ft. The door is 2.5 ft by 6.5 ft.
1)Find the area of the walls and ceiling to be painted.
2)one gallon of paint covers 75.86 square feet, how many gallons?
3)$17.68 a gallon,how much to paint?
Have you found the area of the walls?
64.37
To find the area of the walls and ceiling that need to be painted, follow these steps:
1) Calculate the area of the walls:
- The length of the room is 14 ft.
- The width of the room is 21 ft.
Therefore, the total area of the four walls is (14 + 21) * 2 = 70 ft * 2 = 140 ft.
2) Calculate the area of the ceiling:
- The length of the room is 14 ft.
- The width of the room is 21 ft.
Therefore, the area of the ceiling is 14 * 21 = 294 ft.
3) Calculate the area of the windows:
- There are two windows, and each window measures 3 ft * 4 ft.
Therefore, the total area of the windows is 2 * (3 * 4) = 24 ft.
4) Calculate the area of the door:
- The area of the door is 2.5 ft * 6.5 ft = 16.25 ft.
5) Calculate the total area to be painted:
- Subtract the area of the windows and door from the total area of the walls and ceiling.
- Total area to be painted = (140 + 294) - (24 + 16.25) = 393.75 ft.
To calculate the number of gallons needed, divide the total area by the coverage per gallon:
6) Number of gallons of paint needed:
- Number of gallons = Total area / Coverage per gallon
- Number of gallons = 393.75 ft / 75.86 ft/gallon = 5.18 gallons (rounded to the nearest whole gallon).
To calculate the cost, multiply the number of gallons by the cost per gallon:
7) Cost of paint:
- Cost = Number of gallons * Cost per gallon
- Cost = 5.18 gallons * $17.68/gallon = $91.36.
Therefore, you will need approximately 5.18 gallons of paint, and the total cost to paint the room will be $91.36.
To find the area of the walls and ceiling that need to be painted, you need to calculate the area of each surface separately and then add them together.
1) Area of the walls:
- The width of the room is 14ft, and the height of the walls (from floor to ceiling) is 8ft. So, the total length of the walls is 14ft + 14ft + 21ft + 21ft = 70ft.
- The area of the walls can be calculated by multiplying the length by the height: 70ft * 8ft = 560 square feet.
2) Area of the ceiling:
- The length of the ceiling is the same as the width of the room, which is 14ft.
- The width of the ceiling is the same as the length of the room, which is 21ft.
- The area of the ceiling can be calculated by multiplying the length by the width: 14ft * 21ft = 294 square feet.
Therefore, the total area of the walls and ceiling to be painted is 560 square feet + 294 square feet = 854 square feet.
To calculate the number of gallons of paint needed, you divide the total area by the coverage rate of one gallon of paint.
3) Number of gallons of paint:
- One gallon of paint covers 75.86 square feet.
- Divide the total area (854 square feet) by the coverage rate of one gallon: 854 square feet / 75.86 square feet = 11.25 (approximately).
Therefore, you will need approximately 11.25 gallons of paint.
To calculate the cost of the paint, you multiply the number of gallons needed by the price per gallon.
4) Cost of paint:
- The price per gallon is $17.68.
- Multiply the number of gallons needed (11.25) by the price per gallon: 11.25 gallons * $17.68/gallon = $198.90 (approximately).
Therefore, it will cost approximately $198.90 to paint the room.