# Difference between revisions of "2005 AMC 10A Problems/Problem 11"

(added problem and solution) |
|||

Line 5: | Line 5: | ||

==Solution== | ==Solution== | ||

− | Since there are <math>n^2</math> | + | Since there are <math>n^2</math> little [[face]]s on each face of the big wooden [[cube]], there are <math>6n^2</math> little faces painted red. |

− | Since each unit cube has <math>6</math> faces, there are <math>6n^3</math> faces. | + | Since each unit cube has <math>6</math> faces, there are <math>6n^3</math> little faces total. |

− | Since one-fourth of the faces are painted red, | + | Since one-fourth of the little faces are painted red, |

<math>\frac{6n^2}{6n^3}=\frac{1}{4}</math> | <math>\frac{6n^2}{6n^3}=\frac{1}{4}</math> | ||

Line 15: | Line 15: | ||

<math>\frac{1}{n}=\frac{1}{4}</math> | <math>\frac{1}{n}=\frac{1}{4}</math> | ||

− | <math>n=4\ | + | <math>n=4\Longrightarrow \mathrm{(B)}</math> |

==See Also== | ==See Also== | ||

Line 23: | Line 23: | ||

*[[2005 AMC 10A Problems/Problem 12|Next Problem]] | *[[2005 AMC 10A Problems/Problem 12|Next Problem]] | ||

+ | |||

+ | [[Category:Introductory Geometry Problems]] |

## Revision as of 10:54, 2 August 2006

## 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,