1997 AMC 8 Problem 24
Attempt Problem 24 of the 1997 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 1997 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
24.
Diameter is divided at in the ratio The two semicircles, and divide the circular region into an upper (shaded) region and a lower region. The ratio of the area of the upper region to that of the lower region is
Answer: C
Small hint:
Compare the upper region as a large semicircle minus one small semicircle plus the other
Big hint:
Choose convenient lengths in the ratio
Solution:
Choose so that and The large semicircle has radius so its area is
The semicircle on has radius and area while the semicircle on has radius and area
The upper shaded region has area
The whole circle has area so the lower region has area
The desired ratio is
Thus, C is the correct answer.
Problem 24 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
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