A room is 11ft by 21ft and it needs painted. The ceiling is 8ft above the floor. There are two windows in the room, each is 3ft by 4ft. The door is 2.5ft by 6.5ft.
a)Find the area the walls and ceiling to be painted.
b)One gallon of paint covers 72.63 sq ft. How many gallons needed to paint the room?
c)At $22.77 a gallon, what is the cost to paint the room?
* The area of the walls and the ceiling to be painted is?___________
L = 21 Ft
W = 11 Ft
h = 8 Ft.
a. A=2(W*h)+2(L*h)+(L*W)-2(3*4)-(2.5*6.5).
A=176 + 336 + 231-24-16.25=703 Ft^2 =
Area to be painted.
b. Gal = 703Ft^2 / 72.63Ft^2/gal = 9.7.
c. Cost = 22.77/gal * 9.7gal = $220.40.
To find the area of the walls and ceiling to be painted, we need to calculate the individual areas of each surface and then add them together.
a) The area of the walls can be calculated by finding the perimeter of the room and multiplying it by the height of the walls:
Perimeter of the room = 2 * (length + width)
Perimeter of the room = 2 * (11ft + 21ft) = 64ft
Area of the walls = Perimeter of the room * height of the walls
Area of the walls = 64ft * 8ft = 512sq ft
The area of the ceiling can be calculated by multiplying the length by the width of the room:
Area of the ceiling = length * width
Area of the ceiling = 11ft * 21ft = 231sq ft
Therefore, the total area of the walls and the ceiling to be painted is:
Area of the walls + Area of the ceiling = 512sq ft + 231sq ft = 743sq ft
Thus, the area of the walls and the ceiling to be painted is 743 square feet.
b) To determine how many gallons of paint are needed, we divide the total area to be painted by the coverage per gallon.
Total gallons of paint needed = Total area to be painted / Coverage per gallon
Total gallons of paint needed = 743sq ft / 72.63sq ft ≈ 10.22
Therefore, approximately 10.22 gallons of paint are needed to paint the room.
c) To calculate the cost of painting the room, we multiply the number of gallons needed by the cost per gallon.
Cost to paint the room = Total gallons of paint needed * Cost per gallon
Cost to paint the room = 10.22 gallons * $22.77/gallon
Therefore, the cost to paint the room would be approximately $232.65.