The inner circumference of a circular track is 220 m and the width of the track is 7 m. Calculate the cost of putting up a fence along the outer circle of the track at the rate of Rs. 50 per m.

Options

A. `24,200`
B. `23,200`
C. `13,200`
D. `18,200`

Answer

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

### Step 1: Find the radius of the inner circle
We know the inner circumference of the circular track is given as 220 m. The formula for the circumference \( C \) of a circle is:
\[ C = 2\pi r \]
where \( r \) is the radius.

Given:
\[ 2\pi r_1 = 220 \]
Using the value of \( \pi \approx \frac{22}{7} \):
\[ 2 \times \frac{22}{7} \times r_1 = 220 \]

### Step 2: Rearranging the equation to find \( r_1 \)
To isolate \( r_1 \), we can rearrange the equation:
\[ r_1 = \frac{220 \times 7}{2 \times 22} \]
Calculating the right side:
\[ r_1 = \frac{1540}{44} = 35 \text{ m} \]

### Step 3: Find the radius of the outer circle
The width of the track is given as 7 m. Therefore, the radius of the outer circle \( r_2 \) can be calculated as:
\[ r_2 = r_1 + \text{width} = 35 + 7 = 42 \text{ m} \]

### Step 4: Calculate the circumference of the outer circle
Using the radius of the outer circle, we can find its circumference:
\[ C_{outer} = 2\pi r_2 = 2 \times \frac{22}{7} \times 42 \]
Calculating:
\[ C_{outer} = 2 \times \frac{22}{7} \times 42 = \frac{44 \times 42}{7} = \frac{1848}{7} = 264 \text{ m} \]

### Step 5: Calculate the cost of fencing
The cost of putting up a fence is given as Rs. 50 per meter. Therefore, the total cost can be calculated as:
\[ \text{Total Cost} = \text{Cost per meter} \times \text{Circumference of outer circle} \]
\[ \text{Total Cost} = 50 \times 264 = Rs. 13200 \]

### Final Answer
The total cost of putting up a fence along the outer circle of the track is **Rs. 13,200**.

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