Problem

Solid A is an \(8~\text{cm}~by~3~\text{cm}~by~2~\text{cm}\) rectangular prism. Solid B's net has two \(8\text{-}by-3\), two \(8\text{-}by-2\), and two \(3\text{-}by-2\) rectangles. Calculate \(\text{both}~\text{surface}~\text{areas}\), and compare them.

A neutral labeled rectangular prism and an unlabeled six-face net with dimensions 8 centimeters, 3 centimeters, and 2 centimeters.

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Compare the solid and the net by inventorying their faces rather than their layouts. If both contain the same two copies of each dimension pair, they must share one surface-area expression because folding changes only arrangement, not area. Evaluate that common face-pair sum in square centimeters to confirm the comparison.

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Solid A: 8×3+8×2+3×2=46 cm²; Solid B: 8×3+8×2+3×2=46 cm²; They have the same surface area.

Solid A: 2(8×3)+2(8×2)+2(3×2)=92 cm²; Solid B: 2(8×3)+2(8×2)+2(3×2)=92 cm²; They have the same surface area.

Solid A: 2(8×3)+(8×2)+(3×2)=70 cm²; Solid B: 2(8×3)+(8×2)+(3×2)=70 cm²; They have the same surface area.

Solid A: 2(8×3)+2(8×2)+2(3×2)=92 cm²; Solid B: 8×3+8×2+3×2=46 cm²; They do not have the same surface area.

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Solid A is an \(8~\text{cm}~by~3~\text{cm}~by~2~\text{cm}\) rectangular prism. Solid B's net has two \(8\text{-}by-3\), two \(8\text{-}by-2\), and two \(3\text{-}by-2\) rectangles. Calculate \(\text{both}~\text{surface}~\text{areas}\), and compare them.

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