2013 AMC 10A Problems/Problem 14
Revision as of 16:12, 17 July 2018 by Scrabbler94 (talk | contribs) (→Solution: alternate solution)
Contents
[hide]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
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 12 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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.