Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Put both geometry situations into one modeling language
Problem
Situation A is paper covering a \(12~\text{cm}\) by \(8~\text{cm}\) by \(5~\text{cm}\) box. Situation B is the capacity of a cylinder with radius \(4~\text{cm}\) and height \(10~\text{cm}\). Which complete response correctly compares the situations?
Big Picture
What this problem is really about
Classify each context before calculating: paper covering every box face is a two-dimensional exterior measure, while a can’s capacity is a three-dimensional interior measure. Use the matching face-area and base-area-times-height formulas, then inspect the units. Square centimeters and cubic centimeters describe different dimensions, so their numerical values cannot be ranked directly.
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