The area of a circular field is 13.86 hectares. Find the cost of fencing the field at the rate of Rs 4.40 per metre (assume pi = 22/7).

Introduction / Context:
This question tests circle mensuration with unit conversion and a practical cost calculation. The fencing required equals the circumference of the field. The area is given in hectares, so we must convert to square metres before using the area formula A = pi*r^2 to find the radius. Once radius is known, circumference C = 2*pi*r gives the fence length in metres. Finally, multiply by the rate (Rs per metre) to get the total cost. Using pi = 22/7 helps produce neat numbers if the data is designed for it.

Given Data / Assumptions:

• Area = 13.86 hectares
• 1 hectare = 10000 sq m
• pi = 22/7
• Fencing rate = Rs 4.40 per metre

Concept / Approach:
Convert area to sq m, solve for r from A = pi*r^2, compute circumference C = 2*pi*r, then cost = C * 4.40.

Step-by-Step Solution:
Area in sq m = 13.86 * 10000 = 138600 A = (22/7)*r^2 => r^2 = 138600 * 7 / 22 138600/22 = 6300, so r^2 = 6300*7 = 44100 r = sqrt(44100) = 210 m Circumference C = 2*(22/7)*210 = 1320 m Cost = 1320 * 4.40 = 5808

Verification / Alternative check:
Check area: (22/7)*210^2 = (22/7)*44100 = 22*6300 = 138600 sq m, which matches the converted area, so r and C are consistent.

Why Other Options Are Wrong:
2808, 3808, 4808 occur if circumference or rate multiplication is done incorrectly. 6808 is too high and suggests using a larger circumference or a wrong unit conversion.

Common Pitfalls:
Forgetting hectare conversion, using diameter as radius, using C = pi*r instead of 2*pi*r, or multiplying by Rs 4.40 incorrectly.

Final Answer:
The cost of fencing is Rs 5808.