Grazing area: A cow is tethered with a rope and can graze 9856 sq m. Assuming a circular grazing path, find the length of the rope.

Introduction / Context:This classic geometry problem links area of a circle to its radius, modeling the rope length as the radius of the grazing circle.

Given Data / Assumptions:

• Area A = 9856 sq m
• Grazing path is circular
• Use π = 22/7 unless specified

Concept / Approach:Area A = πr^2 → r = sqrt(A/π). The rope length equals r.

Step-by-Step Solution:

Verification / Alternative check:Area with r = 56: πr^2 = (22/7)*56*56 = (22/7)*3136 = 22*448 = 9856. Perfect match.

Why Other Options Are Wrong:16m, 14m, 76m, 64m do not square to 3136 when used with π = 22/7 to produce 9856 m^2.

Common Pitfalls:Using diameter instead of radius, or incorrect π handling during division.

Final Answer:56m