Grazing rope — A cow must graze an area of 154 sq m. Find the required rope length (assume a circular patch).

Introduction / Context:
When an animal is tethered by a rope of length r to a fixed point, the reachable grazing region is a circle of radius r. Thus, the grazing area equals πr^2, allowing us to solve for r given the area.

Given Data / Assumptions:

• Area = 154 sq m
• π ≈ 22/7 (for neat integers)
• Area A = πr^2

Concept / Approach:
Compute r from r^2 = A / π. With π = 22/7, the numbers are designed to give an integer r.

Step-by-Step Solution:
r^2 = 154 / (22/7) = 154 * 7 / 22 = 49 ⇒ r = 7 m

Verification / Alternative check:
Check: A = (22/7) * 49 = 154 sq m, matching the target area.

Why Other Options Are Wrong:
6, 8, 12, 13 m yield areas not equal to 154 sq m under A = πr^2.

Common Pitfalls:
Forgetting the relationship A = πr^2 or mixing up circumference with area.

Final Answer:
7 m