Cube A has a side length of 4 centimeters (cm). Cube B has a surface area of 54 cm². What...

1. TRANSLATE the problem information

• Given information:
  • Cube A: side length = 4 cm
  • Cube B: surface area = 54 cm²
  • Need: total surface area of both cubes

• What this tells us: We have different types of information for each cube and need to find a sum.

2. INFER the approach

• For Cube A: We have the side length, so we need to calculate surface area using the formula
• For Cube B: Surface area is already given - no calculation needed
• Strategy: Find Cube A's surface area, then add both surface areas

3. SIMPLIFY to find Cube A's surface area

• Apply the formula: \(\mathrm{SA} = 6\mathrm{s}^2\)
• \(\mathrm{SA}_\mathrm{A} = 6 \times (4)^2\)
  \(= 6 \times 16\)
  \(= 96 \text{ cm}^2\)

4. Add both surface areas

• Total \(\mathrm{SA} = \mathrm{SA}_\mathrm{A} + \mathrm{SA}_\mathrm{B}\)
  \(= 96 + 54\)
  \(= 150 \text{ cm}^2\)

Answer: D (150)

Why Students Usually Falter on This Problem

Most Common Error Path:

Missing conceptual knowledge: Doesn't remember the cube surface area formula \(\mathrm{SA} = 6\mathrm{s}^2\)

Without this formula, students cannot calculate Cube A's surface area. They might guess that surface area equals \(4 \times 4 = 16 \text{ cm}^2\) (confusing with area of one face), leading to a total of \(16 + 54 = 70 \text{ cm}^2\). Since 70 isn't an answer choice, this leads to confusion and guessing.

Second Most Common Error:

Weak INFER skill: Unnecessarily trying to find Cube B's side length first

Students might think they need to find Cube B's side length by solving \(54 = 6\mathrm{s}^2\), getting \(\mathrm{s} = 3 \text{ cm}\), then recalculating the surface area. This wastes time and creates opportunities for arithmetic errors, potentially leading them to select Choice A (78) if they make calculation mistakes along the way.

The Bottom Line:

This problem tests whether students can work efficiently with given information - using what's provided directly rather than over-complicating the solution.