A company is wrapping rectangular gift boxes. \(\text{One}~\text{box}\) measures \(12~\text{in}\). by \(8~\text{in}\). by \(5~\text{in}\)., and the goal is to find how much paper covers the entire outside of \(\text{one}~\text{box}\). Evaluate statements A–H, then report the complete set of statements that model the situation correctly.
A. Find surface area using \(2(lw~+~lh~+~\text{wh})\), and report the result in \(\text{square}~\text{inches}\).
B. Find volume using \(\text{lwh}\), because wrapping paper fills the box.
C. \(2(12\cdot~8~+~12\cdot~5~+~8\cdot~5)\) correctly represents the calculation.
D. \(12~+~8~+~5\) gives the amount of wrapping paper needed.
E. Report the final result in \(\text{cubic}~\text{inches}\).
F. Covering the outside requires area, not volume.
G. A valid setup is \(2(12~+~8)~+~2(12~+~5)~+~2(8~+~5)\).
H. The result gives the \(\text{inches}~\text{of}~\text{ribbon}\) needed around the edges.
What this problem is really about
Test every statement against the physical job: wrapping paper covers all six exterior faces of a closed rectangular prism. A correct model must use three pairs of rectangular face areas, preserve multiplication within each face, and report square units. Reject models of inside capacity, edge length, or ribbon distance even if they use all three dimensions.