A road 3.5 m wide surrounds a circular plot whose circumference is 44 m . Find the cost of paving the road at \( ₹ 20 \) per \( \mathrm{m}^{2} \). (Take \( \pi=\frac{22}{7} \) )

To determine the cost of paving the road surrounding the circular plot, follow these steps: 1. **Find the Radius of the Inner Circle (Plot):** Given the circumference of the inner circle: \[ \text{Circumference} = 44 \, \text{m} = 2\pi r_{\text{inner}} \] Solving for \( r_{\text{inner}} \): \[ r_{\text{inner}} = \frac{44}{2\pi} = \frac{44}{2 \times \frac{22}{7}} = 7 \, \text{m} \] 2. **Determine the Outer Radius:** The road is 3.5 m wide, so: \[ r_{\text{outer}} = r_{\text{inner}} + 3.5 = 7 + 3.5 = 10.5 \, \text{m} \] 3. **Calculate the Area of the Road:** The area of the road is the area of the outer circle minus the area of the inner circle: \[ \text{Area} = \pi \left( r_{\text{outer}}^2 - r_{\text{inner}}^2 \right) \] Substituting the values: \[ \text{Area} = \frac{22}{7} \left( 10.5^2 - 7^2 \right) = \frac{22}{7} \left( 110.25 - 49 \right) = \frac{22}{7} \times 61.25 = 192.5 \, \text{m}^2 \] 4. **Compute the Cost of Paving:** Given the cost is ₹20 per m²: \[ \text{Total Cost} = 192.5 \times 20 = ₹3,850 \] **Final Answer:** ₹ 3,850