Problem:
An artist has cubes, each with an edge of meter. She stands them on the ground to from a sculpture as shown. She then paints the exposed surface of the sculpture. How many square meters does she paint?
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Answer Choices:
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Solution:
There are faces exposed on each of the four sides for a total of square meters. From above, there are a total of square meters exposed since the cubes in the second and third layers essentially cover the unexposed portion of the bottom layer. So there are a total of square meters to paint.
The bottom layer has complete faces, four " faces", and four " faces". The second layer has 8 complete faces and four " faces". The top layer has complete faces. The total, then, is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions