The inner circumference of a circular track is 330 m. The track is 10.5 m wide everywhere. Calculate the cost of putting up a fence along the outer circle at the rate of Rs.20 per metre. 

Answer

To solve the problem step by step, we will follow the necessary calculations to find the cost of putting up a fence along the outer circle of the track.

### Step 1: Find the Inner Radius
The inner circumference of the circular track is given as 330 m. We can use the formula for the circumference of a circle:

\[ C = 2\pi r \]

Where \(C\) is the circumference and \(r\) is the radius. Rearranging the formula to find the radius gives us:

\[ r = \frac{C}{2\pi} \]

Substituting the given circumference:

\[ r = \frac{330}{2 \times \frac{22}{7}} = \frac{330 \times 7}{44} = \frac{2310}{44} = 52.5 \text{ m} \]

### Step 2: Find the Outer Radius
The width of the track is given as 10.5 m. To find the outer radius, we add the width of the track to the inner radius:

\[ \text{Outer Radius} = \text{Inner Radius} + \text{Width} = 52.5 \text{ m} + 10.5 \text{ m} = 63 \text{ m} \]

### Step 3: Calculate the Outer Circumference
Now, we will calculate the outer circumference using the outer radius:

\[ \text{Outer Circumference} = 2\pi \times \text{Outer Radius} \]

Substituting the outer radius:

\[ \text{Outer Circumference} = 2 \times \frac{22}{7} \times 63 = \frac{44 \times 63}{7} = \frac{2772}{7} = 396 \text{ m} \]

### Step 4: Calculate the Cost of the Fence
The cost of putting up a fence is given at the rate of Rs. 20 per meter. Therefore, we can calculate the total cost as follows:

\[ \text{Cost} = \text{Outer Circumference} \times \text{Cost per meter} \]

Substituting the values:

\[ \text{Cost} = 396 \text{ m} \times 20 \text{ Rs/m} = 7920 \text{ Rs} \]

### Final Answer
The cost of putting up a fence along the outer circle is Rs. 7920.

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