A rectangular storage bin has dimensions 8 inches by 5 inches by 6 inches. The bin has no top, so...

1. TRANSLATE the problem information

• Given information:
  • Rectangular storage bin: 8 inches by 5 inches by 6 inches
  • No top, so only bottom + four side faces remain
• What this tells us: We need to find the area of exactly 5 faces (not all 6)

2. INFER the approach

• Calculate the area of each remaining face separately
• Add all face areas together for total surface area
• Strategy: Bottom face + 2 long sides + 2 short sides

3. Calculate the bottom face area

• Bottom dimensions: \(\mathrm{8 \times 5 = 40}\) square inches

4. SIMPLIFY the side face calculations

• Two long side faces: Each has dimensions \(\mathrm{8 \times 6}\)
  • Area per face: \(\mathrm{8 \times 6 = 48}\) square inches
  • Total for both: \(\mathrm{2 \times 48 = 96}\) square inches
• Two short side faces: Each has dimensions \(\mathrm{5 \times 6}\)
  • Area per face: \(\mathrm{5 \times 6 = 30}\) square inches
  • Total for both: \(\mathrm{2 \times 30 = 60}\) square inches

5. SIMPLIFY to find the total

• Total surface area = \(\mathrm{40 + 96 + 60 = 196}\) square inches

Answer: B (196)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students miss the key phrase "no top" and calculate all 6 faces instead of just the 5 remaining faces.

They calculate: Bottom (40) + Top (40) + Four sides (96 + 60) = 236 square inches

This leads them to select Choice D (236)

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors in the multiple calculations, especially when doubling the side face areas or adding the final sum.

Common calculation mistakes include confusing which dimensions go together (like using \(\mathrm{8\times5}\) for a side face instead of \(\mathrm{8\times6}\)), leading to incorrect intermediate values and ultimately wrong final answers.

The Bottom Line:

This problem tests careful reading comprehension combined with systematic organization of multiple calculations. Success requires both accurately identifying which faces exist and methodically calculating each area without arithmetic errors.