The area enclosed by a circular plot is \( 61659 . m \). Eind the diavatery of the plot. Also find the cost of fencing it at the rate of \( ₹ 7 \) per.m2

Certainly! Let's solve the problem step-by-step. ### **Given:** - **Area of the circular plot (A)** = \( 61,659 \, \text{m}^2 \) - **Cost of fencing** = ₹ 7 per meter ### **1. Finding the Diameter of the Plot** The area of a circle is given by the formula: \[ A = \pi r^2 \] where: - \( r \) = radius of the circle - \( \pi \) ≈ 3.1416 **Step 1:** Solve for the radius (\( r \)): \[ r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{61,659}{3.1416}} \approx \sqrt{19,636.7} \approx 140.1 \, \text{meters} \] **Step 2:** Calculate the diameter (\( D \)): \[ D = 2r = 2 \times 140.1 \approx 280.2 \, \text{meters} \] **So, the diameter of the plot is approximately **\( 280.2 \, \text{meters} \). --- ### **2. Calculating the Cost of Fencing** The cost of fencing depends on the perimeter (circumference) of the circular plot. The circumference (\( C \)) of a circle is: \[ C = 2\pi r = \pi D \] **Using the diameter:** \[ C = \pi D = 3.1416 \times 280.2 \approx 880 \, \text{meters} \] **Cost Calculation:** \[ \text{Total Cost} = \text{Circumference} \times \text{Cost per meter} = 880 \times 7 = ₹6,160 \] **Therefore, the cost of fencing the plot is ₹ 6,160.** --- ### **Summary:** - **Diameter of the plot:** ≈ 280.2 meters - **Cost of fencing:** ₹ 6,160