Difference between revisions of "2005 AMC 12A Problems/Problem 10"
(New page: == Problem == 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...) |
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== Problem == | == Problem == | ||
| − | 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> | ||
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</math> | </math> | ||
== Solution == | == Solution == | ||
| − | There are <math>6n^3</math> sides total, and <math>6n^2</math> are painted red. | + | There are <math>6n^3</math> sides total on the unit cubes, and <math>6n^2</math> are painted red. |
<math>\dfrac{6n^2}{6n^3}=\dfrac{1}{4} \Rightarrow n=4 \rightarrow \mathrm {B}</math> | <math>\dfrac{6n^2}{6n^3}=\dfrac{1}{4} \Rightarrow n=4 \rightarrow \mathrm {B}</math> | ||
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== See also == | == See also == | ||
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 21:19, 3 July 2013
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
There are 
sides total on the unit cubes, and 
are painted red.
See also
| 2005 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 9 |
Followed by Problem 11 |
| 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 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
