2020 AMC 8 Problem 9
Attempt Problem 9 of the 2020 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
9.
Akash’s birthday cake is in the form of a inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into smaller cubes, each measuring inch, as shown below. How many small pieces will have icing on exactly two sides?
Answer: D
Small hint:
Separate the top layer from the other layers
Big hint:
Top edge pieces and lower corner pieces are the exactly-two-sided pieces
Video solution:
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Written solution:
In the top layer, the non-corner edge pieces have icing on exactly two sides. There are edges with such pieces each, for pieces.
In each of the other layers, the only pieces with exactly two iced sides are the corner pieces. This adds pieces.
The total is
Thus, the correct answer is D.
Problem 9 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
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
- 2002 AMC 8
- 2003 AMC 8
- 2004 AMC 8
- 2005 AMC 8
- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
- 2009 AMC 8
- 2010 AMC 8
- 2011 AMC 8
- 2012 AMC 8
- 2013 AMC 8
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- 2015 AMC 8
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- 2019 AMC 8
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- 2026 AMC 8