A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at Rs 50 per `m^(2)`

Answer

To solve the problem step-by-step, we will follow the outlined process to find the cost of paving the road surrounding a circular plot.

### Step 1: Find the radius of the circular plot
Given the circumference of the circular plot is 44 meters, 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.

Substituting the given circumference:

\[ 44 = 2 \times \frac{22}{7} \times r \]

Now, we can solve for \( r \):

\[ r = \frac{44 \times 7}{2 \times 22} = \frac{308}{44} = 7 \text{ meters} \]

### Step 2: Find the outer radius of the road
The width of the road is given as 3.5 meters. Thus, the outer radius \( R \) can be calculated as:

\[ R = r + \text{width} = 7 + 3.5 = 10.5 \text{ meters} \]

### Step 3: Calculate the area of the road
The area of the road can be found by subtracting the area of the inner circle (the circular plot) from the area of the outer circle (the circular plot plus the road).

The area of a circle is given by the formula:

\[ \text{Area} = \pi r^2 \]

So, the area of the outer circle is:

\[ \text{Area}_{\text{outer}} = \pi R^2 = \pi (10.5)^2 = \frac{22}{7} \times 110.25 = \frac{22 \times 110.25}{7} = \frac{2425.5}{7} \approx 346.5 \text{ m}^2 \]

And the area of the inner circle is:

\[ \text{Area}_{\text{inner}} = \pi r^2 = \pi (7)^2 = \frac{22}{7} \times 49 = 22 \times 7 = 154 \text{ m}^2 \]

Now, the area of the road is:

\[ \text{Area}_{\text{road}} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} = 346.5 - 154 = 192.5 \text{ m}^2 \]

### Step 4: Calculate the cost of paving the road
The cost of paving the road is given as Rs. 50 per square meter. Therefore, the total cost can be calculated as:

\[ \text{Cost} = \text{Area}_{\text{road}} \times \text{Cost per m}^2 = 192.5 \times 50 = 9625 \text{ Rs} \]

### Final Answer
The cost of paving the road is Rs. 9625.

---