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

(Solution)
m (Video Solution)
Line 16: Line 16:
  
 
<math>n=4\Longrightarrow \mathrm{(B)}</math>
 
<math>n=4\Longrightarrow \mathrm{(B)}</math>
 
==Video Solution==
 
CHECK OUT Video Solution: https://youtu.be/mnMsCKv0VVA
 
  
 
==See also==
 
==See also==

Revision as of 15:36, 8 December 2020

Problem

A wooden cube $n$ units on a side is painted red on all six faces and then cut into $n^3$ unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is $n$?

$\mathrm{(A) \ } 3\qquad \mathrm{(B) \ } 4\qquad \mathrm{(C) \ } 5\qquad \mathrm{(D) \ } 6\qquad \mathrm{(E) \ } 7$

Solution

Since there are $n^2$ little faces on each face of the big wooden cube, there are $6n^2$ little faces painted red.

Since each unit cube has $6$ faces, there are $6n^3$ little faces total.

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

$\frac{6n^2}{6n^3}=\frac{1}{4}$

$\frac{1}{n}=\frac{1}{4}$

$n=4\Longrightarrow \mathrm{(B)}$

See also

2005 AMC 10A (ProblemsAnswer KeyResources)
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. AMC logo.png