Glued Cubes
Geometry
Level
3
Three cubes of volume 1, 8 and 27 are glued together along their faces. What is the smallest possible surface area of the resulting configuration?
The answer is 72.
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1 solution
If we want to get the minimal surface area, we can glue the 3×3×3 cube and the 2×2×2 cube first and the unit cube to both (same face of the biggest cube, next to the middle cube).
The resulting surface area:
6 × ( 3 2 + 2 2 + 1 2 ) − 2 × 2 2 − 4 × 1 2 = 7 2