2014 AMC 8 Problem 19
Attempt Problem 19 of the 2014 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 2014 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
A cube with -inch edges is to be constructed from smaller cubes with -inch edges. Twenty-one of the cubes are colored red and are colored white.
If the -inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white?
Answer: A
Small hint:
Hide one white cube in the center of the cube.
Big hint:
Put the remaining white cubes in face centers to expose only one white face each.
Solution:
To minimize visible white area, place one white cube in the center of the large cube, where no faces are visible. Place each of the other five white cubes at the center of a face of the large cube, where each contributes only one visible white square.
The visible white surface area is therefore square inches. The total surface area of the -inch cube is square inches, so the fraction that is white is .
Thus, A is the correct answer.
Problem 19 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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- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
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