1987 AMC 12 Problem 13
Attempt Problem 13 of the 1987 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 1987 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
13.
A long piece of paper cm wide is made into a roll for cash registers by wrapping it times around a cardboard tube of diameter cm, forming a roll cm in diameter. Approximate the length of the paper in meters. (Pretend the paper forms concentric circles with diameters evenly spaced from cm to cm.)
Answer: A
Small hint:
The diameters form an arithmetic sequence
Big hint:
Use the average diameter to find the sum of all circumferences
Solution:
The average of the first and last diameters is Hence the total length is approximately cm, or meters.
Thus the correct answer is A.
Problem 13 in other years
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