Problem 3 · 2021 Math Kangaroo
Medium
Geometry & Measurement
areaarea-decomposition
A cube with edge 1 is cut into two identical cuboids. What is the surface area of one of these cuboids?
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Answer: D — \(4\)
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Hint 1 of 2
A cut parallel to a face splits the cube into two equal boxes; write down the box's dimensions.
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Hint 2 of 2
Add the areas of all six faces of one box.
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Approach: find the dimensions, then total the six faces
- Cutting the unit cube in half gives a box measuring 1 × 1 × ½.
- Its faces: two 1×1 faces (area 1 each) and four 1×½ faces (area ½ each).
- Total surface area = 2·1 + 4·½ = 2 + 2 = 4.
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