2014 AMC 8
Complete problem set with solutions and individual problem pages
Problem 19 Hard
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?
- A.
- B.
- C.
- D.
- E.
Answer:A
For the least possible surface area that is white, we should have 1 cube in the center, and the other 5 with only 1 face exposed. This gives 5 square inches of white, surface area. Since the cube has a surface area of 54 square inches, our answer is .
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