A room is 9 m long, 8 m broad and 6.5 m high. It has one door of dimensions `(2 mxx1.5 m)` and four windows each of dimensions `(1.5 mxx1 m)`. Find the cost of whitewashing the walls at Rs. 25 per `m^(2)`.

Answer

To solve the problem step by step, we will calculate the total area of the walls of the room, subtract the areas of the door and windows, and then find the cost of whitewashing.

### Step 1: Calculate the total surface area of the four walls of the room.

The room has two pairs of opposite walls. The dimensions of the room are:
- Length (L) = 9 m
- Breadth (B) = 8 m
- Height (H) = 6.5 m

The area of the two longer walls (length x height) is:
\[ \text{Area of two longer walls} = 2 \times (L \times H) = 2 \times (9 \, \text{m} \times 6.5 \, \text{m}) \]

Calculating this:
\[ 2 \times (9 \times 6.5) = 2 \times 58.5 = 117 \, \text{m}^2 \]

The area of the two shorter walls (breadth x height) is:
\[ \text{Area of two shorter walls} = 2 \times (B \times H) = 2 \times (8 \, \text{m} \times 6.5 \, \text{m}) \]

Calculating this:
\[ 2 \times (8 \times 6.5) = 2 \times 52 = 104 \, \text{m}^2 \]

Now, adding both areas together:
\[ \text{Total wall area} = 117 \, \text{m}^2 + 104 \, \text{m}^2 = 221 \, \text{m}^2 \]

### Step 2: Calculate the area of the door and windows.

The area of the door is:
- Dimensions of the door = 2 m x 1.5 m
\[ \text{Area of the door} = 2 \, \text{m} \times 1.5 \, \text{m} = 3 \, \text{m}^2 \]

The area of one window is:
- Dimensions of one window = 1.5 m x 1 m
\[ \text{Area of one window} = 1.5 \, \text{m} \times 1 \, \text{m} = 1.5 \, \text{m}^2 \]

Since there are four windows:
\[ \text{Total area of windows} = 4 \times 1.5 \, \text{m}^2 = 6 \, \text{m}^2 \]

### Step 3: Subtract the areas of the door and windows from the total wall area.

Now we subtract the areas of the door and windows from the total wall area:
\[ \text{Required area for whitewashing} = \text{Total wall area} - \text{Area of door} - \text{Total area of windows} \]

Calculating this:
\[ \text{Required area} = 221 \, \text{m}^2 - 3 \, \text{m}^2 - 6 \, \text{m}^2 = 221 - 9 = 212 \, \text{m}^2 \]

### Step 4: Calculate the cost of whitewashing.

The cost of whitewashing is given as Rs. 25 per m². Therefore, the total cost is:
\[ \text{Total cost} = \text{Required area} \times \text{Cost per m}^2 \]
\[ \text{Total cost} = 212 \, \text{m}^2 \times 25 \, \text{Rs/m}^2 = 5300 \, \text{Rs} \]

### Final Answer:
The total cost of whitewashing the walls is **Rs. 5300**.

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