What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a...

1. TRANSLATE the problem information

• Given information:
  • Right rectangular prism
  • Length = 4 centimeters
  • Width = 9 centimeters
  • Height = 10 centimeters
• Find: Volume in cubic centimeters

2. INFER the approach needed

• Since we need volume of a rectangular prism, we use the volume formula
• Volume = \(\mathrm{length \times width \times height}\)
• We multiply all three dimensions together

3. Calculate the volume

• \(\mathrm{V = l \times w \times h}\)
• \(\mathrm{V = 4 \times 9 \times 10}\)
• \(\mathrm{V = 360}\) cubic centimeters

Answer: \(\mathrm{360}\) cubic centimeters

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about volume vs. surface area: Students sometimes confuse volume calculations with surface area calculations, especially if they recently studied surface area formulas. Instead of multiplying the three dimensions, they might try to find the area of each face and add them together.

This leads to confusion and potentially getting stuck on the problem or guessing at an answer.

The Bottom Line:

While this appears to be a straightforward problem, students can get confused if they mix up volume and surface area concepts, or if they don't clearly remember that volume of a rectangular prism requires multiplying all three dimensions together.