A right rectangular prism has a length of 11 meters, a width of 8 meters, and a height of 10...

1. TRANSLATE the problem information

• Given information:
  • Length = 11 meters
  • Width = 8 meters
  • Height = 10 meters
  • Need to find: volume in cubic meters

2. TRANSLATE to identify the approach

• The problem asks for volume of a right rectangular prism
• This means we need the volume formula: \(\mathrm{V = ℓwh}\)
• Where \(\mathrm{ℓ = length}\), \(\mathrm{w = width}\), \(\mathrm{h = height}\)

3. SIMPLIFY by substituting and calculating

• Substitute the given values into \(\mathrm{V = ℓwh}\):
  • \(\mathrm{V = (11)(8)(10)}\)
• Calculate step by step:
  • First: \(\mathrm{11 × 8 = 88}\)
  • Then: \(\mathrm{88 × 10 = 880}\)

Answer: 880

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual gap: Doesn't remember the volume formula for rectangular prisms

Students might confuse this with surface area formulas or simply not recall that volume equals length × width × height. Without the correct formula, they cannot proceed systematically and end up guessing.

Second Most Common Error:

Weak SIMPLIFY execution: Makes arithmetic errors during multiplication

Even with the correct setup \(\mathrm{V = 11 × 8 × 10}\), students might calculate incorrectly. Common mistakes include:

• \(\mathrm{11 × 8 = 80}\) (instead of 88), leading to \(\mathrm{80 × 10 = 800}\)
• Forgetting to multiply by all three dimensions

The Bottom Line:

This is a straightforward application problem that tests whether students know the basic volume formula and can perform multi-step multiplication accurately. The conceptual demand is low, making computational accuracy the primary challenge.