# 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