Difference between revisions of "2013 AMC 10A Problems/Problem 14"
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A solid cube of side length <math>1</math> is removed from each corner of a solid cube of side length <math>3</math>. How many edges does the remaining solid have? | A solid cube of side length <math>1</math> is removed from each corner of a solid cube of side length <math>3</math>. How many edges does the remaining solid have? | ||
<math> \textbf{(A) }36\qquad\textbf{(B) }60\qquad\textbf{(C) }72\qquad\textbf{(D) }84\qquad\textbf{(E) }108\qquad </math> | <math> \textbf{(A) }36\qquad\textbf{(B) }60\qquad\textbf{(C) }72\qquad\textbf{(D) }84\qquad\textbf{(E) }108\qquad </math> | ||
| − | + | [[Category: Introductory Geometry Problems]] | |
== Solution == | == Solution == | ||
Revision as of 10:49, 13 August 2014
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 
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. 
