2006 AMC 8 Problems/Problem 18
Problem
A cube with 3-inch edges is made using 27 cubes with 1-inch edges. Nineteen of the smaller cubes are white and eight are black. If the eight black cubes are placed at the corners of the larger cube, what fraction of the surface area of the larger cube is white?
Solution
The surface area of the cube is 
. Each of the eight black cubes has 3 faces on the outside, making 
black faces. Therefore there are 
white faces. To find the ratio, we evaluate 
.
Solution 2 buttface
We can notice that each face is the same, so each face is 
white.
See Also butt
| 2006 AMC 8 (Problems • Answer Key • Resources) | ||
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Followed by Problem 19 | |
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