A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 75 paise per sq m is

Options

A. A) Rs. 258
B. B) Rs. 358
C. C) Rs. 458
D. D) Rs. 558

Answer

To find the cost of plastering the walls and bottom of the tank, we need to follow these steps:

### Step 1: Calculate the dimensions of the tank
- Length (L) = 25 m
- Width (W) = 12 m
- Depth (H) = 6 m

### Step 2: Calculate the lateral surface area of the tank
The lateral surface area (LSA) of a rectangular tank can be calculated using the formula:
\[ \text{LSA} = 2 \times (L \times H + W \times H) \]

Substituting the values:
\[ \text{LSA} = 2 \times (25 \times 6 + 12 \times 6) \]
\[ \text{LSA} = 2 \times (150 + 72) \]
\[ \text{LSA} = 2 \times 222 \]
\[ \text{LSA} = 444 \, \text{m}^2 \]

### Step 3: Calculate the area of the bottom of the tank
The area of the bottom (A) is given by:
\[ A = L \times W \]
Substituting the values:
\[ A = 25 \times 12 \]
\[ A = 300 \, \text{m}^2 \]

### Step 4: Calculate the total area to be plastered
The total area to be plastered (TAP) is the sum of the lateral surface area and the area of the bottom:
\[ \text{TAP} = \text{LSA} + A \]
\[ \text{TAP} = 444 + 300 \]
\[ \text{TAP} = 744 \, \text{m}^2 \]

### Step 5: Calculate the cost of plastering
The cost of plastering per square meter is given as 75 paise, which is equivalent to:
\[ \text{Cost per sq m} = \frac{75}{100} = 0.75 \, \text{rupees} \]

Now, calculate the total cost (TC):
\[ \text{TC} = \text{TAP} \times \text{Cost per sq m} \]
\[ \text{TC} = 744 \times 0.75 \]
\[ \text{TC} = 558 \, \text{rupees} \]

### Final Answer
The total cost of plastering the walls and bottom of the tank is **558 rupees**.

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