A tank 20m long, 12m wide and 8m 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 2.5m wide.

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the Surface Area of the Tank
The tank is in the shape of a cuboid and is open at the top. The dimensions given are:
- Length (L) = 20 m
- Width (B) = 12 m
- Depth (H) = 8 m

The surface area of the tank (which includes the four sides and the base) can be calculated using the formula:
\[ \text{Surface Area} = \text{Curved Surface Area} + \text{Base Area} \]

**Curved Surface Area (CSA)** of the cuboid is given by:
\[ \text{CSA} = 2 \times (L + B) \times H \]
Substituting the values:
\[ \text{CSA} = 2 \times (20 + 12) \times 8 \]
\[ \text{CSA} = 2 \times 32 \times 8 \]
\[ \text{CSA} = 512 \, \text{m}^2 \]

**Base Area (BA)** is given by:
\[ \text{BA} = L \times B \]
Substituting the values:
\[ \text{BA} = 20 \times 12 \]
\[ \text{BA} = 240 \, \text{m}^2 \]

Now, adding both areas together:
\[ \text{Total Surface Area} = \text{CSA} + \text{BA} \]
\[ \text{Total Surface Area} = 512 + 240 \]
\[ \text{Total Surface Area} = 752 \, \text{m}^2 \]

### Step 2: Calculate the Length of the Iron Sheet Required
The width of the iron sheet is given as 2.5 m. To find the length of the iron sheet required, we can use the formula for the area of a rectangle:
\[ \text{Area} = \text{Length} \times \text{Width} \]

Rearranging for Length:
\[ \text{Length} = \frac{\text{Area}}{\text{Width}} \]
Substituting the values:
\[ \text{Length} = \frac{752}{2.5} \]
Calculating this gives:
\[ \text{Length} = 752 \div 2.5 = 300.8 \, \text{m} \]

### 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:
\[ \text{Total Cost} = \text{Length} \times \text{Cost per meter} \]
Substituting the values:
\[ \text{Total Cost} = 300.8 \times 12.50 \]
Calculating this gives:
\[ \text{Total Cost} = 3760 \, \text{Rs} \]

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

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