Wheel Revolutions to Radius — Distance 44 km in 4000 Revolutions (Recovery Applied): A wheel makes 4000 revolutions while moving 44 km. Find the radius of the wheel.
Aptitude
Area
Difficulty: Medium
Choose an option
-
A1.25 m
-
B1.50 m
-
C1.75 m
-
D2.00 m
-
E2.25 m
Answer
Correct Answer: 1.75 m
Explanation
Introduction / Context:The original options listed very large radii in metres that did not align with the computation, suggesting inconsistency. By the Recovery-First Policy, we keep the given distance and revolutions and reconstruct coherent options around the correct result. The problem uses distance = revolutions * circumference and circumference = 2 * π * r.
Given Data / Assumptions:
- Total distance D = 44 km = 44000 m
- Number of revolutions N = 4000
- Circumference C = D / N
- C = 2 * π * r
Concept / Approach:Each revolution covers one circumference. Compute C, then solve for r = C / (2 * π). Keep metres throughout and round sensibly only at the end to match practical answer choices.
Step-by-Step Solution:
C = 44000 / 4000 = 11 m.r = C / (2 * π) = 11 / (2 * π) ≈ 11 / 6.28318 ≈ 1.75 m.Thus, radius ≈ 1.75 m.Verification / Alternative check:
Check: 2 * π * 1.75 ≈ 10.9956 m; 4000 * 10.9956 ≈ 43982 m ≈ 44 km (rounding error acceptable).Why Other Options Are Wrong:
- 1.25 m and 1.50 m yield too small circumferences.
- 2.00 m and 2.25 m yield distances exceeding 44 km.
Common Pitfalls:
- Mistaking diameter for radius; using C = π * d means d = 11/π and r = d/2.
Final Answer:1.75 m.