1997 AMC 8 Problem 21
Attempt Problem 21 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).
21.
Each corner cube is removed from this cube. The surface area of the remaining figure is
Answer: D
Small hint:
The total surface area stays the same
Big hint:
Removing a corner loses three faces and reveals three faces
Solution:
Note that there is one unit cube between any pair of corner cubes, so the removal of each does not affect the others.
When we remove a corner, we are losing three unit squares. We, however, gain these back from the three faces that get uncovered.
This means that removing a corner cube does not change the surface area. The surface area of the original cube is square centimeters.
Thus, D is the correct answer.
Problem 21 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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