Question

A room measures 13 ft by 18 ft. The ceiling is 9 ft above the floor. The door is 3 ft by 7 ft. A gallon of paint will cover 75.3 ft 2. How many gallons of paint are needed to paint the room (including the ceiling and not including the door).

Answer 1

11 gallons of paint.

Explanation:

The total area of the room that will be painted is:

-> Area of 4 walls

-> Area of ceiling

-> Minus the area of the door

(We will not include the floor, as it normally is not painted)

The area of the walls is 2*9*13 + 2*9*18 = 558 ft2

The area of the ceiling is 13 * 18 = 234 ft2

The area of the door is 7*3 = 21 ft2

So the total area is 558 + 234 - 21 = 771 ft2

If each gallon of paint covers 75.3 ft2, we can find the number of gallons needed with a rule of three:

1 gallon -> 75.3 ft2

X gallons -> 771 ft2

1/X = 75.3/771

X = 771/75.3 = 10.239

We will need 11 gallons of paint.

Answer 2

10.23 gallons

Explanation:

A room measures 13 ft by 18 ft. The ceiling is 9 ft above the floor. The door is 3 ft by 7 ft. A gallon of paint will cover 75.3 ft 2. How many gallons of paint are needed to paint the room (including the ceiling and not including the door)

The first thing is to calculate the area of each part of the room.

So:

ceiling = 13 ft * 18 ft = 234 ft ^ 2

Now the walls are 4 walls, 2 of 13 ft and 2 of 18 ft, therefore:

wall 1,2 = 2 * (13 ft * 9 ft) = 234 ft ^ 2

wall 3.4 = 2 * (18 ft * 9 ft) = 324 ft ^ 2

Finally the door, that this area must be subtracted

door = 3 ft * 7 ft = 21 ft ^ 2

In total then we have: 234 - 234 + 324 - 21 = 771 ft

Now to calculate the number of gallons:

771 ft ^ 2 * 1 gallon / 75.3 ft ^ 2 = 10.23 gallons

So they will need a total of 10.23 gallons