A room measures 15 ft by 19 ft. The ceiling is 10 ft. above the floor. The door is 3 ft. by 7 ft. A gallon of paint will cover 78.2 ft2 . How many gallons of paint are needed to paint the room (including the ceiling and not including the door). Round your answer up to the next whole number.
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Thanks Ms. Sue!
To calculate the total area of the room (including the ceiling but not including the door), we need to calculate the area of each wall and the ceiling separately.
The area of one wall can be found by multiplying the length and height of the wall:
Area of one wall = Length × Height
For the given room, one wall measures 15 ft by 10 ft:
Area of one wall = 15 ft × 10 ft = 150 ft²
Since there are four walls in the room (excluding the door), the total area of the walls is:
Total area of walls = 4 × Area of one wall = 4 × 150 ft² = 600 ft²
The area of the ceiling can be found by multiplying the length and width of the ceiling:
Area of ceiling = Length × Width
For the given room, the ceiling measures 15 ft by 19 ft:
Area of ceiling = 15 ft × 19 ft = 285 ft²
Now, we can calculate the total area to be painted by adding the area of the walls and the ceiling:
Total area to be painted = Total area of walls + Area of ceiling
Total area to be painted = 600 ft² + 285 ft² = 885 ft²
Since 1 gallon of paint can cover 78.2 ft², we need to divide the total area to be painted by the coverage of a gallon of paint to determine the number of gallons needed:
Number of gallons needed = Total area to be painted / Coverage of 1 gallon of paint
Number of gallons needed = 885 ft² / 78.2 ft² = 11.31
Since we need to round the answer up to the next whole number, we would need 12 gallons of paint to paint the room (including the ceiling and excluding the door).