A rectangular prism has a volume of 7{,}200 cubic inches. The length of the prism is 24 inches and the...

1. TRANSLATE the problem information

• Given information:
  • Volume = 7,200 cubic inches
  • Length = 24 inches
  • Width = 30 inches
• What we need to find: height in inches

2. INFER the solution strategy

• We have volume and two dimensions, need the third
• Use the volume formula: \(\mathrm{V = length \times width \times height}\)
• Substitute known values and solve for height

3. TRANSLATE into mathematical equation

Set up the equation: \(\mathrm{7,200 = 24 \times 30 \times height}\)

4. SIMPLIFY the calculation

• First multiply the known dimensions: \(\mathrm{24 \times 30 = 720}\)
• The equation becomes: \(\mathrm{7,200 = 720 \times height}\)
• Divide both sides by 720: \(\mathrm{height = 7,200 \div 720 = 10}\)

Answer: 10 inches

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misidentify which dimension they're solving for or mix up the given dimensions in the formula setup.

For example, they might write \(\mathrm{7,200 = 24 \times height \times 30}\) but then forget which variable represents the unknown, leading to setup confusion and arithmetic errors.

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors when calculating \(\mathrm{24 \times 30}\) or when performing the final division.

Common mistakes include calculating \(\mathrm{24 \times 30 = 54}\) (adding instead of multiplying) or making errors in \(\mathrm{7,200 \div 720}\), leading to answers like 1 or 100.

The Bottom Line:

This problem tests whether students can systematically apply the volume formula by substituting known values and isolating the unknown variable. Success depends on careful translation of the word problem and accurate arithmetic execution.