Annulus width from circumferences: A circular road surrounds a circular ground. The difference between outer and inner circumferences is 66 m. What is the road’s width?

Introduction / Context:The “width” of a circular ring (annulus) is the difference of its radii. Differences in circumferences translate directly into differences in radii via the circumference formula, enabling a quick computation.

Given Data / Assumptions:

• Outer radius R, inner radius r
• 2πR − 2πr = 66 m
• Width w = R − r

Concept / Approach:Factor the circumference difference: 2π(R − r) = 66. Divide by 2π to obtain the width directly.

Step-by-Step Solution:2π(R − r) = 66R − r = 66 / (2π) = 33 / π ≈ 33 / 3.142 ≈ 10.5 m

Verification / Alternative check:Using π = 22/7, width = 33 / (22/7) = 10.5 m exactly, confirming the neat fractional structure often used in aptitude questions.

Why Other Options Are Wrong:21 m and 14 m are multiples of the exact width; 7 m and 5.25 m are fractional misreads of the same relation.

Common Pitfalls:Attempting to find radii individually (unnecessary); mixing diameter and radius terms in the circumference formula.

Final Answer:10.5 meters