A cubical carton has a volume of 1728 cubic cm. What is the length, in cm, of the longest straight rod that can be laid inside it? (Take √3 = 1.732.)

The edge is ∛1728 = 12 cm, and the longest rod lies along the space diagonal, a√$3=12\times 1.732=20.78$ cm. The trap 16.97 is the FACE diagonal a√$2=12\times 1.414$, which is the longest rod that fits flat against one side but not through the body of the carton; 12 is the edge itself; $36=3\times 12$ adds the three edges instead of taking the root of the sum of their squares.