2013 AMC 10A Problems/Problem 14
Contents
Problem
A solid cube of side length is removed from each corner of a solid cube of side length . How many edges does the remaining solid have?
Solution 1
We can use Euler's polyhedron formula that says that . We know that there are originally faces on the cube, and each corner cube creates more. . In addition, each cube creates new vertices while taking away the original , yielding vertices. Thus , so
Solution 2
The removal of each cube adds nine additional edges to the solid. Since a cube initially has edges and there are eight vertices, the number of edges will be .
See Also
2013 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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