A cistern from inside is 12.5 m long , 8.5 m broad and 4m high and is open at top. Find the cost of cementing the inside of a cistern at Rs. 24 per sq. m :

Options

A. Rs. 6582
B. Rs. 8256
C. Rs. 7752
D. Rs. 8752

Answer

To solve the problem of finding the cost of cementing the inside of a cistern, we will follow these steps:

### Step 1: Calculate the Area of the Base of the Cistern
The base of the cistern is a rectangle. The area of the base can be calculated using the formula:
\[ \text{Area of base} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 12.5 m
- Breadth = 8.5 m

Calculating the area:
\[ \text{Area of base} = 12.5 \, \text{m} \times 8.5 \, \text{m} = 106.25 \, \text{m}^2 \]

### Step 2: Calculate the Area of the Four Walls
The cistern has four walls, and we need to calculate the area of each pair of opposite walls.

1. **Area of the two longer walls (length x height)**:
\[ \text{Area of two longer walls} = 2 \times (\text{Length} \times \text{Height}) = 2 \times (12.5 \, \text{m} \times 4 \, \text{m}) = 2 \times 50 = 100 \, \text{m}^2 \]

2. **Area of the two shorter walls (breadth x height)**:
\[ \text{Area of two shorter walls} = 2 \times (\text{Breadth} \times \text{Height}) = 2 \times (8.5 \, \text{m} \times 4 \, \text{m}) = 2 \times 34 = 68 \, \text{m}^2 \]

3. **Total area of the four walls**:
\[ \text{Total area of walls} = \text{Area of two longer walls} + \text{Area of two shorter walls} = 100 \, \text{m}^2 + 68 \, \text{m}^2 = 168 \, \text{m}^2 \]

### Step 3: Calculate the Total Area to be Cemented
Since the cistern is open at the top, the total area to be cemented includes the area of the base and the area of the four walls:
\[ \text{Total area} = \text{Area of base} + \text{Total area of walls} = 106.25 \, \text{m}^2 + 168 \, \text{m}^2 = 274.25 \, \text{m}^2 \]

### Step 4: Calculate the Cost of Cementing
The cost of cementing is given at Rs. 24 per square meter. Therefore, the total cost can be calculated as:
\[ \text{Total cost} = \text{Total area} \times \text{Cost per sq. m} = 274.25 \, \text{m}^2 \times 24 \, \text{Rs/m}^2 \]
Calculating the total cost:
\[ \text{Total cost} = 274.25 \times 24 = 6576 \, \text{Rs} \]

### Final Answer
The cost of cementing the inside of the cistern is **Rs. 6576**.

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