Find the capacity of a rectangula cistern in litres whose dimensions are `11.2mxx6mxx5.8m`. Find the area of the iron sheet required to make the cistern.

Answer

To solve the problem step by step, we will find the capacity of the rectangular cistern in liters and the area of the iron sheet required to make the cistern.

### Step 1: Calculate the Volume of the Cistern
The volume \( V \) of a rectangular prism (cistern) can be calculated using the formula:
\[ V = L \times B \times H \]
where:
- \( L = 11.2 \, \text{m} \) (length)
- \( B = 6 \, \text{m} \) (breadth)
- \( H = 5.8 \, \text{m} \) (height)

Substituting the values:
\[ V = 11.2 \times 6 \times 5.8 \]

Calculating:
\[ V = 11.2 \times 6 = 67.2 \]
\[ V = 67.2 \times 5.8 = 389.76 \, \text{m}^3 \]

### Step 2: Convert Volume to Liters
To convert cubic meters to liters, we use the conversion factor \( 1 \, \text{m}^3 = 1000 \, \text{liters} \).
\[ \text{Capacity in liters} = 389.76 \, \text{m}^3 \times 1000 = 389760 \, \text{liters} \]

### Step 3: Calculate the Surface Area of the Cistern
The surface area \( A \) of a rectangular prism is given by the formula:
\[ A = 2(LB + BH + HL) \]

Substituting the values:
\[ A = 2(11.2 \times 6 + 6 \times 5.8 + 5.8 \times 11.2) \]

Calculating each term:
1. \( LB = 11.2 \times 6 = 67.2 \)
2. \( BH = 6 \times 5.8 = 34.8 \)
3. \( HL = 5.8 \times 11.2 = 64.96 \)

Now, summing these areas:
\[ A = 2(67.2 + 34.8 + 64.96) \]
\[ A = 2(166.96) = 333.92 \, \text{m}^2 \]

### Final Answers
- The capacity of the cistern is **389760 liters**.
- The area of the iron sheet required to make the cistern is **333.92 m²**.

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