2013 AMC 10A Problem 14

Attempt Problem 14 of the 2013 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 10A solutions, or check the answer key.

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14.

A solid cube of side length $1$ is removed from each corner of a solid cube of side length $3.$ How many edges does the remaining solid have?

$36$

$60$

$72$

$84$

$108$

Removing the cubes does not remove any edges from the original cube. It only adds edges.

After removing each cube, we can see that $9$ extra edges are added to the solid.

$8$ cubes are removed, which means $8 \cdot 9 = 72$ edges are added to the original $12$ edges, for a total of $72 + 12 = 84$ edges.

Thus, D is the correct answer.