The area of a circular plavground is `88704m`^(2)`. Find the cost of fencing this ground at the rate of 65 per metre

Answer

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

### Step 1: Understand the formula for the area of a circle
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 2: Set up the equation with the given area
We know the area of the circular playground is \( 88704 \, m^2 \). Therefore, we can set up the equation:
\[ \pi r^2 = 88704 \]

### Step 3: Substitute the value of \( \pi \)
We can use \( \pi \approx \frac{22}{7} \) for our calculations. Substituting this into the equation gives:
\[ \frac{22}{7} r^2 = 88704 \]

### Step 4: Solve for \( r^2 \)
To isolate \( r^2 \), we multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 88704 \times \frac{7}{22} \]
Calculating the right side:
\[ r^2 = 88704 \times \frac{7}{22} = 88704 \times 0.31818 \approx 28224 \]

### Step 5: Find the radius \( r \)
Now, we take the square root of both sides to find \( r \):
\[ r = \sqrt{28224} \]
Calculating the square root:
\[ r = 168 \, m \]

### Step 6: Calculate the circumference of the circle
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
Substituting the value of \( \pi \) and \( r \):
\[ C = 2 \times \frac{22}{7} \times 168 \]
Calculating this gives:
\[ C = \frac{44}{7} \times 168 \]
Now, simplifying:
\[ C = 44 \times 24 = 1056 \, m \]

### Step 7: Calculate the cost of fencing
The cost of fencing is given by multiplying the circumference by the cost per meter:
\[ \text{Cost} = C \times \text{Rate} \]
Substituting the values:
\[ \text{Cost} = 1056 \times 65 \]
Calculating this gives:
\[ \text{Cost} = 68640 \, \text{Rs} \]

### Final Answer
The cost of fencing the circular playground is **Rs. 68640**.

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