A water tank is 30 m long, 20 m wide and 12 m deep. It is made of iron sheet which is 3 m wide. The tank is open at the top. If the cost of iron sheet is Rs. 10 per sq m, then the total cost of iron sheet required to build the tank is

Options

A. Rs. 6,000
B. Rs. 8,000
C. Rs. 9,000
D. Rs. 18,000

Answer

To find the total cost of the iron sheet required to build the water tank, we need to follow these steps:

### Step 1: Calculate the Surface Area of the Tank
The tank is a cuboid with the following dimensions:
- Length (L) = 30 m
- Width (W) = 20 m
- Depth (H) = 12 m

Since the tank is open at the top, we will calculate the surface area of the four sides and the bottom only.

The surface area (SA) of a cuboid is given by:
\[ SA = 2(LW + LH + WH) \]

However, since the tank is open at the top, we will modify the formula:
\[ SA = LW + 2(LH + WH) \]

Substituting the values:
- \( LW = 30 \times 20 = 600 \, \text{m}^2 \)
- \( LH = 30 \times 12 = 360 \, \text{m}^2 \)
- \( WH = 20 \times 12 = 240 \, \text{m}^2 \)

Now, substituting these into the surface area formula:
\[ SA = 600 + 2(360 + 240) \]
\[ SA = 600 + 2(600) \]
\[ SA = 600 + 1200 \]
\[ SA = 1800 \, \text{m}^2 \]

### Step 2: Calculate the Total Cost of the Iron Sheet
The cost of the iron sheet is given as Rs. 10 per square meter.

To find the total cost:
\[ \text{Total Cost} = \text{Surface Area} \times \text{Cost per sq m} \]
\[ \text{Total Cost} = 1800 \, \text{m}^2 \times 10 \, \text{Rs/m}^2 \]
\[ \text{Total Cost} = 18000 \, \text{Rs} \]

### Final Answer
The total cost of the iron sheet required to build the tank is Rs. 18000.

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