Two students are building storage boxes in woodworking class. The first student builds a box in the form of a cube with each edge measuring \(60\text{ cm}\). The second student builds a box in the shape of a rectangular prism with width \(w\text{ cm}\), height \(30\text{ cm}\) and depth \(45\text{ cm}\). Surprisingly, each student’s box has the same total surface area.
Determine which student's box has the greatest volume. How much greater is the volume?
Themes: Algebra, Geometry & Measurement