An Ant's Journey
There is a \(4 \times 6 \times 18\) inch cereal box lying on the floor. It was placed face down on one of its \(6 \times 18\) inch face. An ant is located at one of the bottom corners of the box. It wants to reach the opposite bottom corner (of the \(6 \times 18\) face on the floor), by crawling along the outside of the box, or on the floor. The length of the shortest such path is \(R\) inches. What is the value of \(R^2\)?
Details and assumptions
The ant may not crawl under the box.