A certain container has a volume of 3,830,000 cubic centimeters. What is the volume, in cubic meters, of this container?(1...

1. TRANSLATE the problem information

• Given information:
  • Volume: 3,830,000 cubic centimeters
  • Conversion factor: \(1 \text{ meter} = 100 \text{ centimeters}\)
• Need to find: Volume in cubic meters

2. INFER the conversion relationship

• Since we're dealing with volume (cubic units), we need to cube the linear conversion factor
• If \(1 \text{ meter} = 100 \text{ centimeters}\), then:
  \(1 \text{ cubic meter} = (100 \text{ centimeters})^3 = 1,000,000 \text{ cubic centimeters}\)
• This means \(1,000,000 \text{ cubic centimeters} = 1 \text{ cubic meter}\)

3. SIMPLIFY by applying the conversion

• To convert from cubic centimeters to cubic meters, divide by the conversion factor:
  \(3,830,000 ÷ 1,000,000 = 3.83\)
• Therefore: 3.83 cubic meters

Answer: B. 3.83

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students use the linear conversion factor (100) instead of recognizing they need the cubic conversion factor (1,000,000).

They might think: "1 meter = 100 centimeters, so I divide by 100"
→ \(3,830,000 ÷ 100 = 38,300\)... wait, that's not an option
→ Maybe 38.3?

This may lead them to select Choice C (38.3) after incorrectly reasoning about decimal placement.

Second Most Common Error:

Poor TRANSLATE reasoning: Students get confused about conversion direction and multiply instead of divide.

They might calculate: 3,830,000 × something, or get confused about whether larger units mean bigger or smaller numbers.

This leads to confusion and guessing among the remaining choices.

The Bottom Line:

The key insight is recognizing that volume conversions require cubing the linear conversion factor. Students who miss this fundamental relationship between linear and cubic measurements will struggle with all dimensional analysis problems involving area and volume.