Find the area of metal - sheet required to make an open tank of length = 10 m breadth = 7.5 m and depth = 3.8 m.

Answer

To find the area of the metal sheet required to make an open tank with the given dimensions, we will follow these steps:

### Step 1: Understand the dimensions of the tank
The tank has:
- Length (L) = 10 m
- Breadth (B) = 7.5 m
- Depth (H) = 3.8 m

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

Substituting the values:
- \( L = 10 \, \text{m} \)
- \( B = 7.5 \, \text{m} \)
- \( H = 3.8 \, \text{m} \)

Calculating the area:
\[ \text{Area of four walls} = 2 \times (10 \times 3.8 + 7.5 \times 3.8) \]

Calculating each term:
1. \( 10 \times 3.8 = 38 \)
2. \( 7.5 \times 3.8 = 28.5 \)

Now, adding these:
\[ 38 + 28.5 = 66.5 \]

Now multiply by 2:
\[ 2 \times 66.5 = 133 \, \text{m}^2 \]

### Step 3: Calculate the area of the base
The area of the base of the tank is calculated using the formula:
\[ \text{Area of base} = L \times B \]

Substituting the values:
\[ \text{Area of base} = 10 \times 7.5 = 75 \, \text{m}^2 \]

### Step 4: Calculate the total area of the metal sheet required
The total area of the metal sheet required is the sum of the area of the four walls and the area of the base:
\[ \text{Total area} = \text{Area of four walls} + \text{Area of base} \]
\[ \text{Total area} = 133 + 75 = 208 \, \text{m}^2 \]

### Final Answer
The area of the metal sheet required to make the open tank is **208 m²**.

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