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Wheel revolutions over a distance:\nA wheel has diameter 40 cm. How many complete revolutions does it make while traveling 176 m in a straight line?

Difficulty: Easy

Correct Answer: 140

Explanation:


Introduction / Context:
Counting revolutions converts a linear travel distance into “how many circumferences fit into that distance”. Each full revolution covers one circumference of the wheel.


Given Data / Assumptions:

  • Diameter d = 40 cm = 0.40 m.
  • Total distance D = 176 m (straight line, no slipping).
  • Revolutions n = total distance / circumference.


Concept / Approach:
The circumference C of a circle is C = π * d. Once C is known in meters, compute n = D / C and round only if the division is exact for the intended answer. In this case, it yields a near-integer due to π approximation in options.


Step-by-Step Solution:

C = π * d = π * 0.40 = 0.4π m.n = D / C = 176 / (0.4π) = 440 / π ≈ 140.096…Using π ≈ 22/7 ⇒ n = 440 / (22/7) = 440 * 7 / 22 = 140 exactly.


Verification / Alternative check:

Circumference with π = 22/7 is 0.4 * 22/7 = 8.8/7 ≈ 1.257 m; 176 / 1.257 ≈ 140.


Why Other Options Are Wrong:

240, 40, 340 produce incorrect distances when multiplied by the circumference; only 140 aligns with 176 m using standard π approximation.


Common Pitfalls:

Forgetting to convert centimeters to meters.Using diameter directly as the distance per revolution instead of circumference.


Final Answer:

140
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