1986 AMC 12 Problem 18
Attempt Problem 18 of the 1986 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 1986 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
A plane intersects a right circular cylinder of radius forming an ellipse. If the major axis of the ellipse is longer than the minor axis, the length of the major axis is
Answer: E
Small hint:
The minor axis of such an elliptical section is a diameter of the cylinder
Big hint:
Increase that diameter by to obtain the major axis
Solution:
The minor axis of an elliptical plane section of a right circular cylinder is a diameter of the cylinder. Its length is therefore The major axis is longer, so its length is
Thus the correct answer is E.
Problem 18 in other years
- 1950 AMC 12
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