Two cubes of volumes $8 \text{~cm}^3$ and $27 \text{~cm}^3$ are glued together at their faces to form a solid with the smallest possible surface area. What is the number of square centimeters in the surface area of the resulting solid?
Two cubes of volumes $8 \text{~cm}^3$ and $27 \text{~cm}^3$ are glued together at their faces to form a solid with the smallest possible surface area. What is the number of square centimeters in the surface area of the resulting solid?
