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:
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:
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:
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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