2013 AMC 10A Problem 14

Question

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

Each corner removal creates new exposed edges

Count the original cube edges plus the new edges from each removed corner

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.

Problem 14 in other years