2008 AMC 8 Problem 18
Attempt Problem 18 of the 2008 AMC 8 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 2008 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
Two circles that share the same center have radii meters and meters. An aardvark runs along the path shown, starting at and ending at How many meters does the aardvark run?
Answer: E
Small hint:
Break the route into circular arcs and straight radial segments.
Big hint:
A quarter-circle of radius has length .
Solution:
The circumference of a circle is so going a quarter of the way around is
He goes a quarter of the way around the large circle, so this part is meters. He then goes from the larger circle to the smaller circle, which is meters.
He goes a quarter of the way around the smaller circle, so this part is meters. He then goes through the diameter of the smaller circle, which is meters.
He then goes a quarter of the way around the smaller circle, so this part is meters. He finally goes from the smaller circle to the larger circle, which is meters.
The total length is
Thus, the answer is E .
Problem 18 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
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- 1996 AMC 8
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- 1998 AMC 8
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