Wire re-formed: circle (r = 56 cm) to square: A wire forms a circle of radius 56 cm. If re-bent into a square, what is the square’s area?

Introduction / Context:The same wire length (perimeter) is reused: circumference of the circle becomes the perimeter of the square. From the square’s side, compute area.

Given Data / Assumptions:

• Circle radius r = 56 cm ⇒ circumference C = 2πr.
• Square perimeter = C ⇒ side = C/4.

Concept / Approach:Use π = 22/7 (standard in many aptitude problems) for exact integer results here.

Step-by-Step Solution:

Verification / Alternative check:Using π ≈ 3.14 yields ~7729 sq. cm; with 22/7 the conventional exact result is 7744 (matches options).

Why Other Options Are Wrong:Other numbers do not align with perimeter conservation and the typical π = 22/7 convention used for tidy results.

Common Pitfalls:Forgetting to divide circumference by 4 to get the square’s side; mixing up perimeter and area formulae.

Final Answer:7744