The length of the edge of the base of a right square prism is 6 units. The volume of the...

1. TRANSLATE the problem information

• Given information:
  • Right square prism (square base with perpendicular height)
  • Edge length of square base: \(\mathrm{s = 6}\) units
  • Volume: \(\mathrm{V = 2{,}880}\) cubic units
  • Find: height h
• What this tells us: We have a 3D shape with a square base and need to find how tall it is.

2. TRANSLATE the volume relationship

• For a right square prism: Volume = (Base Area) × Height
• Since base is square with edge s: \(\mathrm{Base\ Area = s^2}\)
• Therefore: \(\mathrm{V = s^2h}\)

3. SIMPLIFY to solve for height

• Substitute known values into \(\mathrm{V = s^2h}\):

\(\mathrm{2{,}880 = (6)^2h}\)
\(\mathrm{2{,}880 = 36h}\)

• Divide both sides by 36:

\(\mathrm{h = 2{,}880 \div 36 = 80}\)

Answer: 80

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Confusing different measurements in the problem setup

Students may look at the base edge length of 6 and the calculated base area of 36, then select 36 as their final answer without recognizing that 36 represents the area of the base, not the height. They stop their solution process too early.

This may lead them to select Choice B (36).

Second Most Common Error Path:

Poor SIMPLIFY execution: Arithmetic errors in the division step

When dividing 2,880 by 36, students might make calculation errors, especially if attempting complex mental math or misplacing decimal points. They might also set up the equation incorrectly as \(\mathrm{2{,}880 = 6h}\) instead of \(\mathrm{2{,}880 = 36h}\).

This leads to confusion and potentially guessing among the remaining choices.

The Bottom Line:

This problem tests whether students can distinguish between the different measurements in a 3D geometry problem (base edge length vs. base area vs. height) and execute the algebraic steps carefully. The key insight is recognizing that you need the base area (\(\mathrm{s^2 = 36}\)) as an intermediate step, but the final answer is the height (80).