The area of a circular cricket ground is 24.64 hectares. Find the cost of making rope boundary at the rate of Rs. 5.40 per metre.

Options

A. Rs. 9,600
B. Rs. 9,504
C. Rs. 9,802
D. Rs. 9,802

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Convert hectares to square meters
The area of the circular cricket ground is given as 24.64 hectares. We know that:
1 hectare = 10,000 square meters.

So, we convert hectares to square meters:
\[ \text{Area in square meters} = 24.64 \, \text{hectares} \times 10,000 \, \text{m}^2/\text{hectare} = 246,400 \, \text{m}^2 \]

### Step 2: Use the area formula to find the radius
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
We can rearrange this formula to find the radius \( r \):
\[ r^2 = \frac{A}{\pi} \]
Substituting the area we found:
\[ r^2 = \frac{246,400}{\pi} \quad (\text{using } \pi \approx 3.14) \]
Calculating:
\[ r^2 = \frac{246,400}{3.14} \approx 78,400 \]

Now, we take the square root to find \( r \):
\[ r = \sqrt{78,400} \approx 280 \, \text{meters} \]

### Step 3: Calculate the circumference of the circular ground
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
Substituting the radius we found:
\[ C = 2 \times \pi \times 280 \approx 2 \times 3.14 \times 280 \]
Calculating:
\[ C \approx 1760 \, \text{meters} \]

### Step 4: Calculate the cost of making the rope boundary
The cost of making the rope boundary is given as Rs. 5.40 per meter. Therefore, the total cost \( \text{Cost} \) can be calculated as:
\[ \text{Cost} = \text{Cost per meter} \times \text{Circumference} \]
Substituting the values:
\[ \text{Cost} = 5.40 \times 1760 \]
Calculating:
\[ \text{Cost} = 9504 \, \text{Rs.} \]

### Final Answer
The total cost of making the rope boundary around the cricket ground is Rs. 9504.

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