Square vs circle — A square has side 5 cm which is 13 cm less than the diameter of a circle. Find the approximate area of the circle.

Introduction / Context:Translate the relationship “square side is 13 cm less than the circle’s diameter” to find the circle’s diameter and radius, then compute the circle’s area. We round to the nearest of the provided options.

Given Data / Assumptions:

• Square side = 5 cm
• Square side = diameter − 13 ⇒ diameter = 5 + 13 = 18 cm
• Radius r = 9 cm

Concept / Approach:Area of a circle A = πr^2. With r = 9 cm, A ≈ π * 81. Using π ≈ 22/7 gives a value close to 255 sq cm.

Step-by-Step Solution:A ≈ (22/7) * 81 ≈ 254.57 sq cmRounded to nearby option ≈ 255 sq cm

Verification / Alternative check:Using π = 3.1416 gives A ≈ 254.47, which is again closest to 255 among the choices.

Why Other Options Are Wrong:245, 235, 265, and 275 sq cm are farther from the true value; 255 is the best approximation.

Common Pitfalls:Subtracting 13 from the radius instead of from the diameter; squaring 18 instead of 9 for the area calculation.

Final Answer:255 sq cm