A tank 20 m long, 12 m wide and 8 m deep is to be made of iron sheet. It is open at the top. Determine the cost of iron-sheet, at the rate of Rs. 12.50 per metre, if the sheet is 2.5 m wide.

Answer

To solve the problem step by step, we will calculate the surface area of the tank, determine the length of the iron sheet needed, and then find the total cost of the iron sheet.

### Step 1: Calculate the surface area of the tank
The tank is open at the top, so we need to calculate the area of the four walls and the base.

1. **Area of the four walls**:
- The formula for the area of the four walls is:
\[ \text{Area of four walls} = 2 \times H \times (L + B) \]
- Where:
- \( H = 8 \, \text{m} \) (height)
- \( L = 20 \, \text{m} \) (length)
- \( B = 12 \, \text{m} \) (breadth)

- Plugging in the values:
\[ \text{Area of four walls} = 2 \times 8 \times (20 + 12) = 2 \times 8 \times 32 = 512 \, \text{m}^2 \]

2. **Area of the base**:
- The formula for the area of the base is:
\[ \text{Area of base} = L \times B \]
- Plugging in the values:
\[ \text{Area of base} = 20 \times 12 = 240 \, \text{m}^2 \]

3. **Total surface area of the tank**:
- Now, we add the area of the four walls and the area of the base:
\[ \text{Total surface area} = \text{Area of four walls} + \text{Area of base} = 512 + 240 = 752 \, \text{m}^2 \]

### Step 2: Determine the length of the iron sheet needed
The iron sheet is 2.5 m wide. To find the length of the iron sheet required, we can use the formula:
\[ \text{Length of iron sheet} = \frac{\text{Total surface area}}{\text{Width of iron sheet}} \]
Plugging in the values:
\[ \text{Length of iron sheet} = \frac{752}{2.5} = 300.8 \, \text{m} \]

### Step 3: Calculate the cost of the iron sheet
The cost of the iron sheet is given as Rs. 12.50 per meter. Therefore, the total cost can be calculated as:
\[ \text{Total cost} = \text{Length of iron sheet} \times \text{Cost per meter} \]
Plugging in the values:
\[ \text{Total cost} = 300.8 \times 12.50 = 3760 \, \text{Rs} \]

### Final Answer
The total cost of the iron sheet required to make the tank is **Rs. 3760**.

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