1950 AMC 12 Problem 33
Attempt Problem 33 of the 1950 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 1950 AMC 12 solutions, or check the answer key.
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33.
The number of circular pipes with an inside diameter of inch which will carry the same amount of water as a pipe with an inside diameter of inches is:
Answer: D
Small hint:
Water-carrying capacity is proportional to cross-sectional area
Big hint:
Circular area scales as the square of the diameter
Solution:
The ratio of the diameters is so the ratio of cross-sectional areas is Thus of the smaller pipes have the same total cross-sectional area as the larger pipe.
Thus, the correct answer is D.