To determine the minimum number of paint cans needed, we can follow these steps:

Step 1: Calculate the total surface area of the walls

The room has 4 walls, and two dimensions are given:

• Two walls of size: $4m \times 3m$
• Two walls of size: $3m \times 3m$

For the two larger walls: $\text{Area of one wall} = 4m \times 3m = 12 \, m^2$ $\text{Area of two larger walls} = 12 \, m^2 \times 2 = 24 \, m^2$

For the two smaller walls: $\text{Area of one wall} = 3m \times 3m = 9 \, m^2$ $\text{Area of two smaller walls} = 9 \, m^2 \times 2 = 18 \, m^2$

Step 2: Calculate the area of the window and door

The window size is $60cm \times 40cm$, which we convert to meters: $\text{Window area} = 0.6m \times 0.4m = 0.24 \, m^2$

The door size is $70cm \times 200cm$, which we convert to meters: $\text{Door area} = 0.7m \times 2m = 1.4 \, m^2$

Step 3: Calculate the total paintable area

The total surface area of the walls is: $\text{Total wall area} = 24 \, m^2 + 18 \, m^2 = 42 \, m^2$

Subtract the area of the window and door: $\text{Total paintable area} = 42 \, m^2 - (0.24 \, m^2 + 1.4 \, m^2) = 42 \, m^2 - 1.64 \, m^2 = 40.36 \, m^2$

Step 4: Calculate the number of paint cans needed

Each can of paint covers 6 square meters, so we divide the total paintable area by the coverage of one can: $\text{Number of cans} = \frac{40.36 \, m^2}{6 \, m^2} = 6.73$ Since we can't buy a fraction of a can, we round up: $\text{Minimum number of cans} = 7$

Conclusion:

The minimum number of paint cans needed is 7.

Would you like further clarification or details on any part of the process?

Here are 5 related questions:

1. How would the calculation change if the window or door sizes were different?
2. What would happen if the coverage of each paint can changed?
3. How does the shape of the room impact the paint required?
4. How would we account for ceilings or floors in a full painting job?
5. What methods could reduce the total amount of paint needed?

Tip: When calculating areas for painting, always remember to exclude non-paintable surfaces like windows and doors.