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.

Difficulty: Easy

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 m


Verification / 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

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