If total cost of fencing a circular plot is Rs. 2816, then what will be cost of fencing a square plot, which has I side of 6.4 meters more than radius of given circular plot having area of `98.56 m^(2).` (consider per meter cost of fencing of circular plot & of square plot same)

Options

A. 3860 Rs.
B. 3820 Rs.
C. 3840 Rs.
D. 3800 Rs.

Answer

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

### Step 1: Find the radius of the circular plot
We know the area of the circular plot is given by the formula:
\[ \text{Area} = \pi r^2 \]
Given that the area is \(98.56 \, m^2\), we can set up the equation:
\[ \pi r^2 = 98.56 \]
To find the radius \(r\), we can rearrange the equation:
\[ r^2 = \frac{98.56}{\pi} \]
Using \(\pi \approx 3.14\):
\[ r^2 = \frac{98.56}{3.14} \approx 31.4 \]
Now, taking the square root:
\[ r = \sqrt{31.4} \approx 5.6 \, m \]

### Step 2: Calculate the side of the square plot
The side of the square plot is given to be \(6.4\) meters more than the radius of the circular plot:
\[ \text{Side of square} = r + 6.4 = 5.6 + 6.4 = 12 \, m \]

### Step 3: Find the perimeter of the square plot
The perimeter \(P\) of a square is given by:
\[ P = 4 \times \text{Side} \]
Substituting the side length:
\[ P = 4 \times 12 = 48 \, m \]

### Step 4: Determine the cost of fencing the square plot
We know the total cost of fencing the circular plot is Rs. 2816. The cost per meter of fencing is:
\[ \text{Cost per meter} = \frac{2816}{\text{Circumference of circular plot}} \]
The circumference \(C\) of the circular plot is given by:
\[ C = 2\pi r \]
Substituting the radius:
\[ C = 2 \times 3.14 \times 5.6 \approx 35.44 \, m \]
Now, calculating the cost per meter:
\[ \text{Cost per meter} = \frac{2816}{35.44} \approx 79.5 \, Rs/m \]

Now, using this cost per meter to find the total cost of fencing the square plot:
\[ \text{Cost of fencing square} = \text{Cost per meter} \times \text{Perimeter of square} \]
Substituting the values:
\[ \text{Cost of fencing square} = 79.5 \times 48 \approx 3816 \, Rs \]

### Final Answer
The cost of fencing the square plot will be approximately Rs. 3816.

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