The volume of a rectangular prism can be calculated using the formula V = lwh, where V is the volume,...

1. TRANSLATE the problem information

• Given information:
  • Volume formula: \(\mathrm{V = lwh}\)
  • Base area: \(\mathrm{A = lw}\)
  • Need to find: height \(\mathrm{h}\) in terms of \(\mathrm{V}\) and \(\mathrm{A}\)

2. INFER the solution strategy

• Key insight: Since we know \(\mathrm{A = lw}\), we can substitute this directly into the volume formula
• This will give us an equation with only \(\mathrm{V}\), \(\mathrm{A}\), and \(\mathrm{h}\)

3. SIMPLIFY through substitution

• Start with: \(\mathrm{V = lwh}\)
• Since \(\mathrm{A = lw}\), substitute: \(\mathrm{V = Ah}\)
• Now we have a simple relationship between volume, base area, and height

4. SIMPLIFY to isolate h

• From \(\mathrm{V = Ah}\), divide both sides by \(\mathrm{A}\):
• \(\mathrm{h = \frac{V}{A}}\)

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize that they can substitute \(\mathrm{A = lw}\) into the volume formula. Instead, they try to work directly with \(\mathrm{V = lwh}\) and get confused about how to incorporate the base area \(\mathrm{A}\). This leads to confusion and guessing among the answer choices.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(\mathrm{V = Ah}\) but make algebraic errors when solving for \(\mathrm{h}\). They might incorrectly think \(\mathrm{h = \frac{A}{V}}\) (confusing which variable goes in the numerator and denominator). This may lead them to select Choice A (\(\mathrm{h = \frac{A}{V}}\)).

The Bottom Line:

This problem tests whether students can recognize that formulas can be rewritten using substitution. The key insight is seeing that \(\mathrm{A = lw}\) isn't just extra information - it's the bridge that simplifies the volume formula into a more manageable form.