A cow is tethered with a rope so that it can graze in a circular region. If the cow must be able to graze an area of 9856 sq m, find the required length of the rope in metres (assume the grazed region is a perfect circle and use pi = 22/7).

Introduction / Context:
This question connects real-life interpretation (rope length) with circle geometry. If the cow is tied to a fixed point, the rope length acts as the radius of the circular grazing area. The area is given, so you use the circle area formula A = pi * r^2 to solve for r. The value of pi is specified (22/7) to avoid approximation differences.

Given Data / Assumptions:

• Grazing area A = 9856 sq m
• Circle area formula: A = pi * r^2
• Rope length = radius r
• Use pi = 22/7

Concept / Approach:
Rearrange A = pi*r^2 to r^2 = A/pi, then compute r by taking square root. The rope length equals the computed radius.

Step-by-Step Solution:

Verification / Alternative check:
Check by forward calculation: area = (22/7) * 56^2 = (22/7) * 3136. Since 3136/7 = 448, area = 22 * 448 = 9856 sq m, matching exactly. So rope length must be 56 m.

Why Other Options Are Wrong:

Common Pitfalls:
Common errors include using circumference 2*pi*r instead of area, forgetting to divide by pi, or making mistakes in fraction division by (22/7). Also, some compute r^2 correctly but forget to take the square root at the end. Always interpret rope length as the radius of the grazed circle.

Final Answer:
56 m