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2013 AMC 10A Problem 14

Problem 14 of 25IntermediateGeometry

A solid cube of side length 11 is removed from each corner of a solid cube of side length 3.3. How many edges does the remaining solid have?

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Solution

Removing the cubes does not remove any edges from the original cube. It only adds edges. After removing each cube, we can see that 99 extra edges are added to the solid. 88 cubes are removed, which means 89=728 \cdot 9 = 72 edges are added to the original 1212 edges, for a total of 72+12=8472 + 12 = 84 edges. Thus, D is the correct answer.

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Concepts: polyhedron · cube geometry

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.