1953 AMC 12 Problem 11

Attempt Problem 11 of the 1953 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1953 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

11.

A running track is the ring formed by two concentric circles. It is 1010 feet wide. The circumferences of the two circles differ by about:
1010 feet
3030 feet
6060 feet
100100 feet
none of these
Answer: C
Concepts:circle circumferenceapproximation
Small hint:
The outer radius is 1010 feet greater than the inner radius
Big hint:
Subtract the circumferences; the unknown inner radius cancels
Solution:
If the inner radius is r,r, the difference is 2π(r+10)−2πr=20π≈62.8 2\pi(r+10)-2\pi r=20\pi\approx62.8 feet, which is about 6060 feet.
Thus, the correct answer is C.
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