Circular track — A cyclist travels one lap (circumference) at 14.4 km/h in 1 min 28 s. Find the field’s area.

Introduction / Context:One full lap around a circular field equals its circumference. Given speed and time, we find the distance per lap (circumference), then radius, and finally the area using A = πr^2.

Given Data / Assumptions:

• Speed = 14.4 km/h = 4 m/s
• Time = 1 min 28 s = 88 s
• Circumference C = speed * time
• π ≈ 22/7 for exact result here

Concept / Approach:Compute C, then r = C / (2π), and area A = πr^2. Numbers are chosen for a clean r.

Step-by-Step Solution:C = 4 * 88 = 352 mr = 352 / (2 * 22/7) = 352 / (44/7) = 352 * 7 / 44 = 56 mA = πr^2 = (22/7) * 56^2 = (22/7) * 3136 = 22 * 448 = 9856 sq m

Verification / Alternative check:With r = 56 m, circumference is 2πr = 2 * (22/7) * 56 = 352 m, which matches the distance covered.

Why Other Options Are Wrong:7958 and 8842 sq m come from rounding or π ≈ 3.14 without keeping the exact nice fraction; “Cannot be determined” is false because data are sufficient.

Common Pitfalls:Not converting km/h to m/s; mixing up diameter and radius in circumference calculations.

Final Answer:9856 sq m