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AMO 2027 Grades 9-11 SET 3 - Self-study Question 4

AMO · AMO 2027 Grades 9-11 SET 3 - Self-study

Question 4

Three cubes with volumes $1\text{ cm}^3$, $8\text{ cm}^3$ and $125\text{ cm}^3$ are glued together to form a solid. What is its least possible surface area, in $\text{cm}^2$? Use the source's face-to-face model: cubes remain intact, do not overlap, and their corresponding edges are parallel; partial face contacts are allowed.

Enter one positive integer, without units.