Difference between revisions of "2005 AMC 10A Problems/Problem 11"
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A wooden cube <math>n</math> units on a side is painted red on all six faces and then cut into <math>n^3</math> unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is <math>n</math>? | A wooden cube <math>n</math> units on a side is painted red on all six faces and then cut into <math>n^3</math> unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is <math>n</math>? | ||
| − | <math> \ | + | <math> \textbf{(A) } 3\qquad \textbf{(B) } 4\qquad \textbf{(C) } 5\qquad \textbf{(D) } 6\qquad \textbf{(E) } 7 </math> |
==Solution== | ==Solution== | ||
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<math>\frac{1}{n}=\frac{1}{4}</math> | <math>\frac{1}{n}=\frac{1}{4}</math> | ||
| − | <math>n= | + | <math>n=\boxed{\textbf{(B) }4}</math> |
| − | |||
| − | |||
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==See also== | ==See also== | ||
Latest revision as of 11:40, 13 December 2021
Problem
A wooden cube 
units on a side is painted red on all six faces and then cut into 
unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is ?
Solution
Since there are 
little faces on each face of the big wooden cube, there are 
little faces painted red.
Since each unit cube has 
faces, there are 
little faces total.
Since one-fourth of the little faces are painted red,
See also
| 2005 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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. 
