2003 AMC 8 Problem 22
Attempt Problem 22 of the 2003 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 2003 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
The following figures are composed of squares and circles. Which figure has a shaded region with largest area?
only
only
only
both and
all are equal
Answer: C
Small hint:
Figures and leave the same shaded area.
Big hint:
For compare with
Solution:
In figure the shaded area is the area of a by square minus a circle of radius so it is
Figure is made of four copies of figure with half the side length, so each copy has one-fourth the area and the total shaded area is also
In figure the circle has radius and the inscribed square has diagonal so its area is The shaded area is
Since we have so figure has the largest shaded area.
Thus, C is the correct answer.
Problem 22 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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