Problem 2 · 2013 Math Kangaroo
Easy
Spatial & Visual Reasoning
cube-views
Nathalie wants to build a large cube out of small cubes (the complete cube is shown on the left). How many small cubes are missing from the shape on the right so that it would form the large cube?
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Answer: C — 7
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Hint 1 of 3
A full \(3\times3\times3\) cube is built from 27 little cubes.
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Hint 2 of 3
Count the little cubes already in the picture on the right, then see how many are still needed.
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Hint 3 of 3
Missing cubes = 27 minus the ones you counted.
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Approach: count present cubes and subtract from a full cube
- The finished big cube is 3 cubes wide, 3 tall and 3 deep, so it needs \(3\times3\times3 = 27\) small cubes.
- Counting the cubes in the picture on the right gives 20.
- So the number still missing is \(27 - 20 = 7\), which is choice C.
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