I have to paint one side of a wall. The wall is 12 meters tall and 120 meters long. Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then what is the smallest whole number of gallons I can buy and have enough paint to cover the whole wall?
First we need to convert the dimensions of the wall from meters to feet:
12 meters = 39.37 feet
120 meters = 393.70 feet
The area of one side of the wall is 39.37 ft x 393.70 ft = 15,489.51 square feet.
We need to convert this into square meters so we can figure out how many gallons of paint we need:
1 square foot = 0.092903 square meters
15,489.51 square feet = 1,439.81 square meters
Each gallon of paint covers 150 square feet, which is 13.94 square meters:
150 square feet = 13.94 square meters
To find out how many gallons of paint we need, we divide the total area of the wall by the coverage per gallon of paint:
1,439.81 square meters ÷ 13.94 square meters/gallon = 103.27 gallons
Since we can't buy a fraction of a gallon, we need to round up to the nearest whole number. Therefore, we need to buy at least 104 gallons of paint to cover the whole wall.
To determine the smallest whole number of gallons needed to paint the wall, we need to find the total area of the wall and then divide it by the coverage of one gallon of paint.
First, let's convert the dimensions of the wall from meters to feet:
Height of the wall = 12 meters = 12 / 0.3048 feet = 39.3701 feet (approximately)
Length of the wall = 120 meters = 120 / 0.3048 feet = 393.7008 feet (approximately)
Next, calculate the total area of the wall:
Area of the wall = Height × Length
Area of the wall = 39.3701 feet × 393.7008 feet
Area of the wall ≈ 15,492.0957 square feet
Now, divide the total area of the wall by the coverage of one gallon of paint:
Number of gallons needed = Total area of the wall / Coverage per gallon
Number of gallons needed = 15,492.0957 square feet / 150 square feet per gallon (rounded down to the nearest whole gallon)
Number of gallons needed = 103.2806 gallons
Since you can't purchase a fraction of a gallon, you would need to buy at least 104 gallons of paint in order to cover the entire wall.