A gift is packaged in a box shaped like a perfect cube. The length of one edge of the box...

1. TRANSLATE the problem information

• Given information:
  • A cube-shaped box with \(\mathrm{edge\ length = 15\ inches}\)
  • Need to find: total surface area in square inches

2. INFER the geometric approach

• A cube has 6 identical square faces (think of a dice - it has 6 faces)
• Total surface area = sum of areas of all 6 faces
• Since all faces are identical: \(\mathrm{Total\ surface\ area = 6 × (area\ of\ one\ face)}\)

3. APPLY the area formula for one square face

• \(\mathrm{Area\ of\ one\ square\ face = side^2}\)
• \(\mathrm{Area\ of\ one\ face = 15^2 = 225\ square\ inches}\)

4. SIMPLIFY to find total surface area

• \(\mathrm{Total\ surface\ area = 6 × 225 = 1,350\ square\ inches}\)

Answer: C. 1,350

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about surface area vs. volume: Students may calculate the volume of the cube instead of surface area.

• They use \(\mathrm{V = side^3 = 15^3 = 3,375}\)
• This gives them the amount of space inside the cube, not the area covering its outer surfaces
• This may lead them to select Choice D (3,375)

Second Most Common Error:

Weak INFER skill: Students calculate the area of only one face and forget to multiply by 6.

• They correctly find area of one face: \(\mathrm{15^2 = 225}\)
• But they stop there, thinking this is the total surface area
• This may lead them to select Choice B (225)

The Bottom Line:

Success requires clearly distinguishing between surface area (covering the outside) and volume (filling the inside), plus recognizing that "total" surface area means adding up all six faces of the cube.