A tank is 25 m long, 12 m wide and 6m deep. The cost (in Rs.) of plastering its walls and bottom at Rs.10 per `m^(2)` is:

Options

A. 11160
B. 12500
C. 6275
D. 7440

Answer

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

### Step 1: Calculate the Surface Area of the Tank

The tank is a rectangular prism, and we need to calculate the surface area of its walls and bottom.

1. **Dimensions of the tank:**
- Length (L) = 25 m
- Width (W) = 12 m
- Depth (H) = 6 m

2. **Surface area of the walls:**
- There are two pairs of opposite walls:
- Two walls of dimensions 25 m (length) x 6 m (height)
- Two walls of dimensions 12 m (width) x 6 m (height)

- Area of the two longer walls:
\[ \text{Area}_{\text{long walls}} = 2 \times (L \times H) = 2 \times (25 \times 6) = 2 \times 150 = 300 \, m^2 \]

- Area of the two shorter walls:
\[ \text{Area}_{\text{short walls}} = 2 \times (W \times H) = 2 \times (12 \times 6) = 2 \times 72 = 144 \, m^2 \]

- Total area of the walls:
\[ \text{Total Area}_{\text{walls}} = \text{Area}_{\text{long walls}} + \text{Area}_{\text{short walls}} = 300 + 144 = 444 \, m^2 \]

3. **Surface area of the bottom:**
- The bottom area is simply the length times the width:
\[ \text{Area}_{\text{bottom}} = L \times W = 25 \times 12 = 300 \, m^2 \]

4. **Total surface area to be plastered:**
\[ \text{Total Surface Area} = \text{Total Area}_{\text{walls}} + \text{Area}_{\text{bottom}} = 444 + 300 = 744 \, m^2 \]

### Step 2: Calculate the Cost of Plastering

Now that we have the total surface area, we can calculate the cost of plastering.

1. **Cost per square meter:**
- Cost = Rs. 10 per m²

2. **Total cost:**
\[ \text{Total Cost} = \text{Total Surface Area} \times \text{Cost per m²} = 744 \times 10 = 7440 \, \text{Rs.} \]

### Final Answer

The cost of plastering the walls and bottom of the tank is Rs. 7440.

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