Answer :
Let's go through the problem step-by-step and calculate the amount of paint needed.
1. Calculate the total area of the walls:
- There are four walls in the room, but we can simplify this by calculating the area of two opposite pairs of walls.
- Area of the two longer walls (length = 7 meters, height = 3 meters):
- Each wall’s area: [tex]\(7 \, \text{m} \times 3 \, \text{m} = 21 \, \text{m}^2\)[/tex]
- Total for two longer walls: [tex]\(2 \times 21 \, \text{m}^2 = 42 \, \text{m}^2\)[/tex]
- Area of the two shorter walls (width = 6 meters, height = 3 meters):
- Each wall’s area: [tex]\(6 \, \text{m} \times 3 \, \text{m} = 18 \, \text{m}^2\)[/tex]
- Total for two shorter walls: [tex]\(2 \times 18 \, \text{m}^2 = 36 \, \text{m}^2\)[/tex]
- Total wall area: [tex]\(42 \, \text{m}^2 + 36 \, \text{m}^2 = 78 \, \text{m}^2\)[/tex]
2. Calculate the total area of the windows and doors:
- Dimensions and total area for all windows:
- Window dimensions: [tex]\(0.5 \, \text{m} \times 0.8 \, \text{m} = 0.4 \, \text{m}^2\)[/tex]
- Number of windows: 4
- Total window area: [tex]\(4 \times 0.4 \, \text{m}^2 = 1.6 \, \text{m}^2\)[/tex]
- Dimensions and total area for all doors:
- Door dimensions: [tex]\(0.8 \, \text{m} \times 2 \, \text{m} = 1.6 \, \text{m}^2\)[/tex]
- Number of doors: 2
- Total door area: [tex]\(2 \times 1.6 \, \text{m}^2 = 3.2 \, \text{m}^2\)[/tex]
3. Calculate the paintable area:
- Paintable area: Total wall area minus the area occupied by windows and doors
- Paintable area: [tex]\(78 \, \text{m}^2 - 1.6 \, \text{m}^2 - 3.2 \, \text{m}^2 = 73.2 \, \text{m}^2\)[/tex]
4. Determine the amount of paint needed:
- Coverage per kilogram of paint: 4 [tex]\( \text{m}^2/\text{kg} \)[/tex]
- Paint needed: [tex]\( \frac{73.2 \, \text{m}^2}{4 \, \text{m}^2/\text{kg}} = 18.3 \, \text{kg} \)[/tex]
Hence, the amount of paint needed is 18.3 kilograms. The correct answer is not matched perfectly with any of the given options directly but closest to the answer.
So, the correct choice would be a rounded figure, depending on the multiple choice options provided. It seems there might be a slight deviation in the calculation in the options provided:
However, if we follow the given options:
a. 18 kg
b. 18.7 kg
Depending on the context, the closest value might be an approximation or there might have been slight in the provided options. Hence you may pick the closest rounded-off option provided within closest tolerance range mentioned (a. 18 kg).
But mathematically the exact needed amount is 18.3 kg based on the detailed calculation as done.
1. Calculate the total area of the walls:
- There are four walls in the room, but we can simplify this by calculating the area of two opposite pairs of walls.
- Area of the two longer walls (length = 7 meters, height = 3 meters):
- Each wall’s area: [tex]\(7 \, \text{m} \times 3 \, \text{m} = 21 \, \text{m}^2\)[/tex]
- Total for two longer walls: [tex]\(2 \times 21 \, \text{m}^2 = 42 \, \text{m}^2\)[/tex]
- Area of the two shorter walls (width = 6 meters, height = 3 meters):
- Each wall’s area: [tex]\(6 \, \text{m} \times 3 \, \text{m} = 18 \, \text{m}^2\)[/tex]
- Total for two shorter walls: [tex]\(2 \times 18 \, \text{m}^2 = 36 \, \text{m}^2\)[/tex]
- Total wall area: [tex]\(42 \, \text{m}^2 + 36 \, \text{m}^2 = 78 \, \text{m}^2\)[/tex]
2. Calculate the total area of the windows and doors:
- Dimensions and total area for all windows:
- Window dimensions: [tex]\(0.5 \, \text{m} \times 0.8 \, \text{m} = 0.4 \, \text{m}^2\)[/tex]
- Number of windows: 4
- Total window area: [tex]\(4 \times 0.4 \, \text{m}^2 = 1.6 \, \text{m}^2\)[/tex]
- Dimensions and total area for all doors:
- Door dimensions: [tex]\(0.8 \, \text{m} \times 2 \, \text{m} = 1.6 \, \text{m}^2\)[/tex]
- Number of doors: 2
- Total door area: [tex]\(2 \times 1.6 \, \text{m}^2 = 3.2 \, \text{m}^2\)[/tex]
3. Calculate the paintable area:
- Paintable area: Total wall area minus the area occupied by windows and doors
- Paintable area: [tex]\(78 \, \text{m}^2 - 1.6 \, \text{m}^2 - 3.2 \, \text{m}^2 = 73.2 \, \text{m}^2\)[/tex]
4. Determine the amount of paint needed:
- Coverage per kilogram of paint: 4 [tex]\( \text{m}^2/\text{kg} \)[/tex]
- Paint needed: [tex]\( \frac{73.2 \, \text{m}^2}{4 \, \text{m}^2/\text{kg}} = 18.3 \, \text{kg} \)[/tex]
Hence, the amount of paint needed is 18.3 kilograms. The correct answer is not matched perfectly with any of the given options directly but closest to the answer.
So, the correct choice would be a rounded figure, depending on the multiple choice options provided. It seems there might be a slight deviation in the calculation in the options provided:
However, if we follow the given options:
a. 18 kg
b. 18.7 kg
Depending on the context, the closest value might be an approximation or there might have been slight in the provided options. Hence you may pick the closest rounded-off option provided within closest tolerance range mentioned (a. 18 kg).
But mathematically the exact needed amount is 18.3 kg based on the detailed calculation as done.
