A closed rectangular box of length, breadth and height are 3 m, 2 m and 1 m respectively. Find the cost of cloth to cover box completely, if 1 `m^2` cloth costs Rs. 10.

Options

A. Rs. 22
B. Rs. 2200
C. Rs. 220
D. Rs. 200

Answer

To find the cost of cloth to cover a closed rectangular box completely, we need to follow these steps:

### Step 1: Identify the dimensions of the box
The dimensions given are:
- Length (L) = 3 m
- Breadth (B) = 2 m
- Height (H) = 1 m

### Step 2: Calculate the total surface area (TSA) of the box
The formula for the total surface area of a rectangular box is:
\[ \text{TSA} = 2(LB + BH + HL) \]
Substituting the values:
\[ \text{TSA} = 2(3 \times 2 + 2 \times 1 + 1 \times 3) \]

### Step 3: Perform the calculations inside the parentheses
Calculate each term:
- \(3 \times 2 = 6\)
- \(2 \times 1 = 2\)
- \(1 \times 3 = 3\)

Now add these results:
\[ 6 + 2 + 3 = 11 \]

### Step 4: Multiply by 2 to find the total surface area
Now, multiply by 2:
\[ \text{TSA} = 2 \times 11 = 22 \, \text{m}^2 \]

### Step 5: Calculate the cost of the cloth
The cost of covering 1 m² of cloth is Rs. 10. Therefore, the cost to cover the total surface area is:
\[ \text{Cost} = \text{TSA} \times \text{Cost per m}^2 = 22 \times 10 \]

### Step 6: Perform the final multiplication
\[ \text{Cost} = 220 \, \text{Rs.} \]

### Final Answer
The cost of cloth to cover the box completely is Rs. 220.

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