The area of a circular field is 13.86 hectares (1 hectare = 10,000 m^2). Find the total fencing cost at Rs 4.40 per metre (use circumference at the boundary).

Introduction / Context:This problem connects area of a circle with its perimeter (circumference) to determine the cost of fencing a circular field. Converting hectares to square metres is essential before using circle formulas.

Given Data / Assumptions:

• Area A = 13.86 hectares = 13.86 * 10,000 = 138,600 m^2.
• Cost per metre = Rs 4.40.
• Fencing length required = circumference = 2 * pi * r.

Concept / Approach:Use A = pi * r^2 to find r. Then circumference C = 2 * pi * r. A direct composite relation eliminates r: C = 2 * sqrt(A * pi). Multiply by cost per metre to get total cost.

Step-by-Step Solution:

Verification / Alternative check:Compute radius first: r = sqrt(A / pi) ≈ sqrt(138,600 / 3.142857...) ≈ 210 m. Then C = 2 * pi * r ≈ 2 * 3.142857... * 210 = 1,320 m. Cost again: 1,320 * 4.40 = Rs 5,808, consistent.

Why Other Options Are Wrong:

• 2808, 3808, 4808: Each corresponds to a much shorter circumference than a 138,600 m^2 circle would have, yielding a radius far too small.

Common Pitfalls:

• Forgetting the hectare to m^2 conversion (factor 10,000).
• Using diameter instead of radius in circumference formula.
• Premature rounding that shifts the final cost band.

Final Answer:5808