Problem 26 · 2025 Math Kangaroo
Stretch
Spatial & Visual Reasoning
areasubstitution
If the height of a cuboid is reduced by 3 cm, its surface area decreases by 60 cm² and the result is a cube. What is the volume of the original cuboid, in cm³?
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Answer: D — 200
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Hint 1 of 2
When you trim 3 cm off the height you remove a band around the side — that lost area is the side perimeter times 3.
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Hint 2 of 2
After trimming it's a cube, so the base is a square; find its side from the lost surface area.
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Approach: relate the surface-area loss to the base perimeter
- Cutting the height by 3 cm removes a strip of lateral surface = (base perimeter)×3 = 60, so the base perimeter is 20 and each square side is 5.
- The result is a cube of side 5, so the original height was 5 + 3 = 8.
- Original volume = \(5\times5\times8 = 200\) cm³, which is (D).
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