Wheel rounds over a fixed distance: A wheel of diameter 7/11 m travels 4 km. How many complete revolutions does it make (no slip)?

Introduction / Context:Counting revolutions requires the circumference. Here, a nice fraction pairs with the common approximation π = 22/7 to produce an exact, tidy circumference, making arithmetic quick and reliable.

Given Data / Assumptions:

• Diameter d = 7/11 m
• Distance L = 4 km = 4000 m
• No slipping; length per revolution = circumference

Concept / Approach:Circumference C = π * d. With π ≈ 22/7, C = (22/7) * (7/11) = 2 m exactly. Revolutions N = L / C.

Step-by-Step Solution:C = 2 m per revolutionN = 4000 / 2 = 2000

Verification / Alternative check:Even with π to more decimals, the figure remains ~2 m; rounding would still lead precisely to 2000 given the crafted fraction in d.

Why Other Options Are Wrong:Values other than 2000 imply a circumference different from ~2 m, contradicting π * d for the given diameter.

Common Pitfalls:Using radius instead of diameter in C = πd; failing to convert 4 km into meters.

Final Answer:2000