A room is 9 m by 8 m by 6.5 m. It has one door of dimensions `(2 m xx 1.5 m)` and four windows each of dimensions `(1.5 mxx1 m)`. Find the cost of painting the walls at 50 per m.

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Surface Area of the Walls
The room has dimensions:
- Length (L) = 9 m
- Breadth (B) = 8 m
- Height (H) = 6.5 m

The surface area of the walls can be calculated using the formula:
\[ \text{Surface Area of Walls} = 2 \times (L + B) \times H \]

Substituting the values:
\[ \text{Surface Area of Walls} = 2 \times (9 + 8) \times 6.5 \]
\[ = 2 \times 17 \times 6.5 \]
\[ = 34 \times 6.5 \]
\[ = 221 \, \text{m}^2 \]

### Step 2: Calculate the Area of the Door
The dimensions of the door are:
- Length = 2 m
- Breadth = 1.5 m

The area of the door is given by:
\[ \text{Area of Door} = \text{Length} \times \text{Breadth} \]
\[ = 2 \times 1.5 = 3 \, \text{m}^2 \]

### Step 3: Calculate the Area of the Windows
Each window has dimensions:
- Length = 1.5 m
- Breadth = 1 m

The area of one window is:
\[ \text{Area of One Window} = \text{Length} \times \text{Breadth} \]
\[ = 1.5 \times 1 = 1.5 \, \text{m}^2 \]

Since there are 4 windows, the total area of the windows is:
\[ \text{Total Area of Windows} = 4 \times \text{Area of One Window} \]
\[ = 4 \times 1.5 = 6 \, \text{m}^2 \]

### Step 4: Calculate the Total Area to be Painted
Now, we will subtract the area of the door and the area of the windows from the surface area of the walls:
\[ \text{Total Area to be Painted} = \text{Surface Area of Walls} - (\text{Area of Door} + \text{Total Area of Windows}) \]
\[ = 221 - (3 + 6) \]
\[ = 221 - 9 \]
\[ = 212 \, \text{m}^2 \]

### Step 5: Calculate the Cost of Painting
The cost of painting is given as Rs. 50 per square meter. Therefore, the total cost is:
\[ \text{Total Cost} = \text{Total Area to be Painted} \times \text{Cost per m}^2 \]
\[ = 212 \times 50 \]
\[ = 10600 \, \text{Rupees} \]

Thus, the cost of painting the walls is **Rs. 10,600**.

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