If the circumference of a circle is 352 meters, find its area in square meters (use π = 22/7).

Introduction / Context:
Circumference gives a direct path to the radius using C = 2πr. Once r is known, the area follows from A = πr^2. With π = 22/7, several common circumference values yield neat, exact radii and areas.

Given Data / Assumptions:

• C = 352 m
• π = 22/7
• Formulas: C = 2πr, A = πr^2

Concept / Approach:
Compute r from r = C / (2π). Then square r and multiply by π to get area in m^2.

Step-by-Step Solution:
r = 352 / (2*(22/7)) = 352 / (44/7) = 352 * 7 / 44 = 56 mA = πr^2 = (22/7) * 56^2 = (22/7) * 3136 = 22 * 448 = 9856 m^2

Verification / Alternative check:
Back-calc C: 2πr = 2*(22/7)*56 = 2*176 = 352 m, consistent with the given circumference.

Why Other Options Are Wrong:
8956, 6589, and 5986 m^2 do not result from the exact radius 56 m under π = 22/7; only 9856 m^2 matches precisely.

Common Pitfalls:
Mistakes often occur when inverting 2π or mishandling the fraction 22/7. Keeping it symbolic until the last step helps avoid arithmetic slips.

Final Answer:
9856