Problem 17 · 1993 AJHSME
Hard
Geometry & Measurement
surface-areanet
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Answer: B — 500.
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Hint 1 of 2
Each corner cut takes 5 off both ends of a side, so the base shrinks by 10 in each direction: 20−10 and 30−10. The 5-wide flaps that fold up become the box's height of 5.
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Hint 2 of 2
An open box has a bottom and 4 walls but NO lid. Add those five faces; don't include a top.
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Approach: unfold the box into bottom + four walls (no top)
- Cutting a 5×5 square from each corner removes 5 from both ends of every side, so the base is (20−5−5) × (30−5−5) = 10 × 20 = 200. The flaps that fold upward are 5 tall, so the box height is 5.
- Four walls: two are 10×5 and two are 20×5, totaling 2(50) + 2(100) = 300. The interior is the bottom plus those four walls (no lid): 200 + 300 = 500.
- Trap to dodge: 'open box' means skip the top — count 5 faces, not 6. And remember the corner cuts subtract from both ends, so the base loses 2×5 in each direction, not just 5. Choice E (1000) is what you'd get from the full original 20×30 sheet's worth of double-counting.
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