Each base of a right rectangular prism has a length of 19 inches and a width of 8 inches. The...

1. TRANSLATE the problem information

• Given information:
  • Length of base: 19 inches
  • Width of base: 8 inches
  • Volume: 2,736 cubic inches
  • Need to find: height

• This gives us everything we need for the volume formula except height

2. TRANSLATE into mathematical equation

• Volume formula: \(\mathrm{V = length \times width \times height}\)
• Substitute known values: \(\mathrm{2,736 = 19 \times 8 \times h}\)

3. SIMPLIFY the equation step by step

• First, calculate the base area: \(\mathrm{19 \times 8 = 152}\)
• So our equation becomes: \(\mathrm{2,736 = 152h}\)
• Solve for height: \(\mathrm{h = 2,736 \div 152 = 18}\) inches

Answer: A. 18

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors during calculations, particularly when computing \(\mathrm{2,736 \div 152}\). Without careful calculation, they might get confused by the large numbers and arrive at incorrect values.

This may lead them to select Choice B (27) or Choice C (144) if they make computational mistakes.

Second Most Common Error:

Conceptual confusion about problem structure: Students might calculate the base area (\(\mathrm{19 \times 8 = 152}\)) correctly but then think this IS the answer they're looking for, confusing area with height.

This may lead them to select Choice D (152) - which the solution explicitly identifies as the base area, not the height.

The Bottom Line:

This problem tests whether students can systematically apply the volume formula and perform accurate calculations with larger numbers. Success requires both understanding what the formula represents and executing the arithmetic precisely.