The inner circumference of a circular race track is 440 m. The track is uniformly 14 m wide (so the outer radius is 14 m more than the inner radius). Find the radius of the outer circle in metres, using pi = 22/7 for calculation consistency.

Difficulty: Medium

Correct Answer: 84 m

Explanation:


Introduction / Context:
This question tests circle circumference and the concept of a uniform-width track. The inner boundary is a circle whose circumference is given. From circumference = 2*pi*r, you find the inner radius. Then add the track width (14 m) to get the outer radius. The important point is that the track width increases the radius, not the diameter.


Given Data / Assumptions:

  • Inner circumference C_inner = 440 m
  • Track width = 14 m
  • Use pi = 22/7
  • Circumference formula: C = 2 * pi * r
  • Outer radius = inner radius + 14


Concept / Approach:
Compute inner radius from 440 = 2*pi*r. Then increase by 14 m to get outer radius. Keep units in metres throughout.


Step-by-Step Solution:

Step 1: 440 = 2 * (22/7) * r_inner Step 2: 2 * (22/7) = 44/7, so 440 = (44/7) * r_inner Step 3: r_inner = 440 * 7 / 44 = 10 * 7 = 70 m Step 4: r_outer = r_inner + 14 = 70 + 14 = 84 m


Verification / Alternative check:
The inner radius 70 m gives inner circumference 2*(22/7)*70 = 2*22*10 = 440 m, correct. Since the track is 14 m wide, moving outward increases the radius by 14 m, so 84 m is consistent and must be the outer radius.


Why Other Options Are Wrong:

70 m: this is the inner radius, not the outer radius. 44 m or 22 m: arise from confusing circumference with radius or using pi incorrectly. 33 m: not consistent with 440 m circumference at all. Any value not equal to 70 + 14 cannot be correct if inner radius is computed correctly.


Common Pitfalls:
A common mistake is adding 14 to the diameter instead of the radius, or subtracting instead of adding. Another error is using C = pi*r instead of 2*pi*r. Always compute inner radius first from the given inner circumference and only then adjust by the track width.


Final Answer:
84 m

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