Outer radius from inner circumference and track width: A circular race track is 14 m wide. The inner circumference is 440 m. What is the radius of the outer circle?

Introduction / Context:
Concentric circles model circular tracks: inner and outer edges are separated by the constant width. With an inner circumference given, we compute the inner radius and add the width to obtain the outer radius.

Given Data / Assumptions:

• Track width w = 14 m
• Inner circumference C_in = 440 m
• Inner radius r_in = C_in / (2π)
• Outer radius r_out = r_in + w

Concept / Approach:
Use r = C / (2π) to get r_in, then add the width. Using π = 22/7 streamlines the arithmetic and yields an exact result often targeted by test setters.

Step-by-Step Solution:
r_in = 440 / (2π) = 220 / π ≈ 220 / (22/7) = 70 mr_out = 70 + 14 = 84 m

Verification / Alternative check:
Check C_out = 2π * 84 ≈ 528π/π? Using 22/7, C_out = 2 * (22/7) * 84 = 528 m, consistent with a 14 m width increment in radius (circumference increases by 2π * 14).

Why Other Options Are Wrong:
70 m is the inner radius; 56 m and 64 m are too small; 77 m ignores adding full width; only 84 m reflects inner radius plus width.

Common Pitfalls:
Subtracting rather than adding the width; using diameter in place of radius when applying circumference.

Final Answer:
84 m