Problem:
A cube is composed of twenty-seven cubes. The big cube is 'tunneled' as follows: First, the six cubes which make up the center of each face as well as the center cube are removed as shown. Second, each of the twenty remaining cubes is diminished in the same way. That is, the center facial unit cubes as well as each center cube are removed.
The surface area of the final figure is
Answer Choices:
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Solution:
After step one, twenty cubes remain, eight of which are corner cubes and twelve of which are edge cubes. At this stage each corner cube contributes units of area and each edge cube contributes units of area. The second stage of the tunneling process takes away units of area from each of the eight corner cubes ( for each exposed surface), but adds units to the area ( units for each of the six center facial cubes removed). The twelve edge cubes each lose units but gain units. Therefore, the total surface area of the figure is