Problem:
A solid cube has side length inches. A -inch by -inch square hole is cut into the center of each face. The edges of each cut are parallel to the edges of the cube, and each hole goes all the way through the cube. What is the volume, in cubic inches, of the remaining solid?
Answer Choices:
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Solution:
The volume of the solid cube is . The first hole to be cut removes from the volume. The other holes remove from each of the four remaining faces. The volume of the remaining solid is .
The problems on this page are the property of the MAA's American Mathematics Competitions