Question 7
Three cubes of volumes $8\text{ cm}^3$, $27\text{ cm}^3$ and $64\text{ cm}^3$ are glued together. What is the least possible surface area of the resulting solid, in $\text{cm}^2$?
**Added editorial restriction for this self-study question:** all cube vertices must lie on one common cubic grid with spacing 1 cm, and all cube edges must be parallel to the grid axes. The cubes are not cut, their interiors do not overlap, and planar face contacts may be partial. This grid restriction is not stated in the original question. Enter the number.
**Added editorial restriction for this self-study question:** all cube vertices must lie on one common cubic grid with spacing 1 cm, and all cube edges must be parallel to the grid axes. The cubes are not cut, their interiors do not overlap, and planar face contacts may be partial. This grid restriction is not stated in the original question. Enter the number.