The inner circumference of a circular track is 132 m. The track is 2.5 m wide everywhere. Calculate the cost of putting up a fence along the outer circle at the rate of 3.50 per metre.

Answer

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

### Step 1: Find the radius of the inner circle
The inner circumference of the circular track is given as 132 m. The formula for the circumference \( C \) of a circle is:
\[ C = 2 \pi r \]
where \( r \) is the radius.

We can rearrange this formula to find the radius:
\[ r = \frac{C}{2 \pi} \]
Substituting the given circumference:
\[ r = \frac{132}{2 \pi} \]

### Step 2: Calculate the radius
Using the value of \( \pi \approx 3.14 \):
\[ r = \frac{132}{2 \times 3.14} = \frac{132}{6.28} \approx 21 \text{ m} \]

### Step 3: Find the radius of the outer circle
The track is 2.5 m wide everywhere, so the radius of the outer circle \( R \) is:
\[ R = r + 2.5 = 21 + 2.5 = 23.5 \text{ m} \]

### Step 4: Calculate the outer circumference
Now we can find the outer circumference using the radius of the outer circle:
\[ C_{\text{outer}} = 2 \pi R = 2 \pi (23.5) \]
Substituting the value of \( R \):
\[ C_{\text{outer}} = 2 \times 3.14 \times 23.5 \approx 147.88 \text{ m} \]

### Step 5: Calculate the cost of the fence
The cost of putting up a fence along the outer circle is calculated by multiplying the outer circumference by the cost per meter:
\[ \text{Cost} = C_{\text{outer}} \times \text{rate} \]
Given that the rate is 3.50 per meter:
\[ \text{Cost} = 147.88 \times 3.50 \approx 517.58 \text{ rupees} \]

### Final Answer
The total cost of putting up a fence along the outer circle is approximately **517.58 rupees**.

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