A tank 30 m long. 24 m wide and 4.5 m deep is to be made. It is open from the top. Find the cost of iron- sheet required at the rate of rupes 65 per ` m^(2) `. To make the tank.

Answer

To solve the problem step by step, we need to find the total surface area of the tank that is open from the top and then calculate the cost of the iron sheet required to cover that area.

### Step 1: Identify the dimensions of the tank
- Length (L) = 30 m
- Width (W) = 24 m
- Depth (H) = 4.5 m

### Step 2: Calculate the area of the four walls
The formula for the lateral surface area (area of the four walls) of a tank is:
\[ \text{Area of four walls} = 2 \times (L \times H + W \times H) \]

Substituting the values:
\[ \text{Area of four walls} = 2 \times (30 \times 4.5 + 24 \times 4.5) \]

Calculating each term:
- \( 30 \times 4.5 = 135 \)
- \( 24 \times 4.5 = 108 \)

Now substituting back:
\[ \text{Area of four walls} = 2 \times (135 + 108) \]
\[ \text{Area of four walls} = 2 \times 243 = 486 \, \text{m}^2 \]

### Step 3: Calculate the area of the base
The area of the base is given by:
\[ \text{Area of base} = L \times W \]
Substituting the values:
\[ \text{Area of base} = 30 \times 24 = 720 \, \text{m}^2 \]

### Step 4: Calculate the total surface area
The total surface area required for the iron sheet is the sum of the area of the four walls and the area of the base:
\[ \text{Total area} = \text{Area of four walls} + \text{Area of base} \]
\[ \text{Total area} = 486 + 720 = 1206 \, \text{m}^2 \]

### Step 5: Calculate the cost of the iron sheet
The cost of the iron sheet is calculated by multiplying the total area by the cost per square meter:
\[ \text{Cost} = \text{Total area} \times \text{Cost per m}^2 \]
Given that the cost is 65 rupees per m²:
\[ \text{Cost} = 1206 \times 65 \]

Calculating this:
- \( 1206 \times 65 = 78,390 \, \text{rupees} \)

### Final Answer
The total cost of the iron sheet required to make the tank is **78,390 rupees**.

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