Problem 6 · 2009 Math Kangaroo
Easy
Spatial & Visual Reasoning
spatial-reasoning
How many faces does the object shown have? (It is a prism with a hole through it.)
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Answer: D — 8
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Hint 1 of 2
Count the outside surfaces first, then remember the hole adds new inside surfaces too.
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Hint 2 of 2
A triangular tube has 3 inner walls plus 3 outer walls, and the two ends are still faces.
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Approach: count outer and inner faces
- The two triangular ends are now frames, but each is still one face: 2 faces.
- The three outer rectangular sides: 3 faces.
- Drilling the triangular hole creates three inner rectangular walls: 3 more faces.
- Total = 2 + 3 + 3 = 8 faces — answer D.
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