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

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<math>n=4\Longrightarrow \mathrm{(B)}</math>
 
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==See Also==
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==See also==
*[[2005 AMC 10A Problems]]
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*[[2005 AMC 10A Problems/Problem 10|Previous Problem]]
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[[Category:Introductory Number Theory Problems]]
 
 
*[[2005 AMC 10A Problems/Problem 12|Next Problem]]
 
 
 
[[Category:Introductory Geometry Problems]]
 
 
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Revision as of 14:32, 13 August 2019

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
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All AMC 10 Problems and Solutions

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