Difference between revisions of "2014 AMC 8 Problems/Problem 19"
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A cube with <math>3</math>-inch edges is to be constructed from <math>27</math> smaller cubes with <math>1</math>-inch edges. Twenty-one of the cubes are colored red and <math>6</math> are colored white. If the <math>3</math>-inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white? | A cube with <math>3</math>-inch edges is to be constructed from <math>27</math> smaller cubes with <math>1</math>-inch edges. Twenty-one of the cubes are colored red and <math>6</math> are colored white. If the <math>3</math>-inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white? | ||
<math> \textbf{(A) }\frac{5}{54}\qquad\textbf{(B) }\frac{1}{9}\qquad\textbf{(C) }\frac{5}{27}\qquad\textbf{(D) }\frac{2}{9}\qquad\textbf{(E) }\frac{1}{3} </math> | <math> \textbf{(A) }\frac{5}{54}\qquad\textbf{(B) }\frac{1}{9}\qquad\textbf{(C) }\frac{5}{27}\qquad\textbf{(D) }\frac{2}{9}\qquad\textbf{(E) }\frac{1}{3} </math> | ||
Revision as of 19:40, 26 November 2014
Problem
A cube with 
-inch edges is to be constructed from 
smaller cubes with 
-inch edges. Twenty-one of the cubes are colored red and 
are colored white. If the -inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white?
