# 1998 AHSME Problem 27

Geometry Level 2

A $$9 \times 9 \times 9$$ cube is composed of twenty-seven $$3 \times 3 \times 3$$ cubes. The big cube is ‘tunneled’ as follows: First the six $$3 \times 3 \times 3$$ cubes which make up the center of each face as well as the center $$3 \times 3 \times 3$$ cube are removed as shown. Second, each of the twenty remaining $$3 \times 3 \times 3$$ 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

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