A monument outside city hall has dimensions as shown in the figure below. If one gallon of paint can cover 189, how many gallons of paint must be bought in order to paint the monument? Assume that the base of the monument cannot be painted and that paint can be bought only by the gallon.
To find the total surface area of the monument that needs to be painted, we need to find the area of each face and then add them all together.
1. Find the area of the front face:
- The front face is a rectangle with dimensions 8 feet by 12 feet.
- The area of a rectangle is given by the formula: length x width.
- Area of the front face = 8 feet x 12 feet = 96 square feet.
2. Find the area of the two side faces:
- Each side face is a rectangle with dimensions 6 feet by 12 feet.
- Area of each side face = 6 feet x 12 feet = 72 square feet.
- Total area of both side faces = 2 x 72 square feet = 144 square feet.
3. Find the area of the top face:
- The top face is a square with sides of length 8 feet.
- Area of a square is given by the formula: side x side.
- Area of the top face = 8 feet x 8 feet = 64 square feet.
4. Add all the areas together to find the total painting area:
- Total area = Front face + 2 side faces + top face
- Total painting area = 96 square feet + 144 square feet + 64 square feet = 304 square feet.
5. Now, find how many gallons of paint are needed to cover this area:
- Since one gallon can cover 189 square feet, divide the total painting area by 189.
- Gallons of paint needed = 304 square feet / 189 square feet/gallon ≈ 1.61 gallons.
Therefore, you would need to buy 2 gallons of paint to paint the monument, as paint can only be bought by the gallon.