Circular race track: The inner circumference of a circular track is 440 m and the track is 14 m wide uniformly. Find the radius of the outer circle of the track.
Aptitude
Area
Difficulty: Easy
Choose an option
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A44
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B22
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C33
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D84
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E70
Answer
Correct Answer: 84
Explanation
Introduction / Context:Concentric circles model a circular track. Inner circumference and uniform width allow computation of inner and then outer radius.
Given Data / Assumptions:
- Inner circumference C_in = 440 m
- Track width w = 14 m
- Use π = 22/7 unless stated otherwise (standard for such questions)
Concept / Approach:For a circle, C = 2 * π * r. First find r_in from C_in, then r_out = r_in + w.
Step-by-Step Solution:
r_in = C_in / (2π) = 440 / (2 * 22/7) = 440 / (44/7) = 440 * 7 / 44 = 70 mr_out = r_in + w = 70 + 14 = 84 mVerification / Alternative check:Compute outer circumference to sense-check: 2 * π * 84 = 2 * (22/7) * 84 = 2 * 22 * 12 = 528 m (plausible given width 14 m).
Why Other Options Are Wrong:44, 22, 33, 70 correspond to inner or unrelated radii; only 84 equals inner plus width.
Common Pitfalls:Forgetting to add width to get outer radius or using diameter instead of radius in the formula.
Final Answer:84