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

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

− | 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 there are <math>n^2</math> little [[face]]s on each face of the big wooden [[cube (geometry) | 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> little faces total. | Since each unit cube has <math>6</math> faces, there are <math>6n^3</math> little faces total. |

## Revision as of 12:30, 30 October 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,