The area of a circular field is 13.86 hectares (1 hectare = 10,000 m^2). Find the cost of fencing it at 20 paisa per meter (i.e., Rs 0.20 per meter).

Introduction / Context:This question requires converting area units, computing the radius from area, determining the circumference (fencing length), and finally multiplying by a cost rate per meter. Using π = 22/7 will keep numbers tidy if the area is chosen to be a perfect multiple.

Given Data / Assumptions:

• Area A = 13.86 hectares = 13.86 * 10,000 = 138,600 m^2
• π = 22/7 (implied by the neat numbers)
• Cost rate = Rs 0.20 per meter

Concept / Approach:From A = πr^2, solve for r: r^2 = A/π. Then circumference C = 2πr gives the total fencing length. Multiply C by the rate to get cost.

Step-by-Step Solution:r^2 = 138,600 / (22/7) = 138,600 * 7 / 22 = 44100r = √44100 = 210 mC = 2πr = 2*(22/7)*210 = 1320 mCost = 1320 * 0.20 = Rs 264

Verification / Alternative check:Back-calc area from r = 210: A = (22/7)*210^2 = (22/7)*44,100 = 138,600 m^2 = 13.86 hectares — consistent.

Why Other Options Are Wrong:Rs 277.20, Rs 324, and Rs 198 correspond to different circumferences not implied by A = 138,600 m^2 with π = 22/7. Only Rs 264 matches the exact computation.

Common Pitfalls:Confusing perimeter with diameter, or forgetting the hectare-to-square-meter conversion, which is crucial here. Also, mixing paisa and rupee values (20 paisa = Rs 0.20) can cause arithmetic slips.

Final Answer:Rs. 264