The length, breadth and height of a hall are 16 m, 10 m and 6 m respectively. It has two doors measuring 2 m `times` 1.5 m each and four windows measuring 2 m `times` 2 m each. Find the cost of white washing all the four walls and the ceiling of the hall at the rate of Rs. 5 per `m^(2)`.

Answer

To find the cost of whitewashing all the four walls and the ceiling of the hall, we will follow these steps:

### Step 1: Calculate the Surface Area of the Hall
The surface area to be whitewashed includes the four walls and the ceiling.

1. **Calculate the area of the four walls:**
- The formula for the area of the four walls is:
\[ \text{Area of walls} = 2 \times (h \times l + h \times b) \]
- Where:
- \( h = 6 \, m \) (height)
- \( l = 16 \, m \) (length)
- \( b = 10 \, m \) (breadth)

- Plugging in the values:
\[ \text{Area of walls} = 2 \times (6 \times 16 + 6 \times 10) \]
\[ = 2 \times (96 + 60) = 2 \times 156 = 312 \, m^2 \]

2. **Calculate the area of the ceiling:**
- The area of the ceiling is simply:
\[ \text{Area of ceiling} = l \times b = 16 \times 10 = 160 \, m^2 \]

3. **Total area before subtracting doors and windows:**
- Total area to be whitewashed:
\[ \text{Total area} = \text{Area of walls} + \text{Area of ceiling} = 312 + 160 = 472 \, m^2 \]

### Step 2: Subtract the Area of Doors and Windows
1. **Calculate the area of the doors:**
- Each door measures \( 2 \, m \times 1.5 \, m \):
\[ \text{Area of one door} = 2 \times 1.5 = 3 \, m^2 \]
- There are 2 doors:
\[ \text{Total area of doors} = 2 \times 3 = 6 \, m^2 \]

2. **Calculate the area of the windows:**
- Each window measures \( 2 \, m \times 2 \, m \):
\[ \text{Area of one window} = 2 \times 2 = 4 \, m^2 \]
- There are 4 windows:
\[ \text{Total area of windows} = 4 \times 4 = 16 \, m^2 \]

3. **Total area of doors and windows:**
\[ \text{Total area of doors and windows} = 6 + 16 = 22 \, m^2 \]

4. **Net area to be whitewashed:**
\[ \text{Net area} = \text{Total area} - \text{Total area of doors and windows} = 472 - 22 = 450 \, m^2 \]

### Step 3: Calculate the Cost of Whitewashing
1. **Cost per square meter:**
- Given that the cost of whitewashing is Rs. 5 per \( m^2 \).

2. **Total cost:**
\[ \text{Total cost} = \text{Net area} \times \text{Cost per } m^2 = 450 \times 5 = 2250 \, \text{Rs.} \]

### Final Answer
The cost of whitewashing all the four walls and the ceiling of the hall is **Rs. 2250**.

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