What volume, in cubic centimeters, is equivalent to a volume of 4 cubic meters?(1 meter = 100 centimeters)

1. TRANSLATE the problem information

• Given information:
  • Volume to convert: \(\mathrm{4\text{ cubic meters}}\)
  • Linear conversion factor: \(\mathrm{1\text{ meter} = 100\text{ centimeters}}\)
  • Need to find: equivalent volume in cubic centimeters

2. INFER the conversion strategy

• Key insight: Volume units are cubic (length³), so when converting volume units, we must cube the linear conversion factor
• We can't just multiply by 100 - that would only work for linear measurements
• For volume: If \(\mathrm{1\text{ meter} = 100\text{ centimeters}}\), then \(\mathrm{1\text{ cubic meter} = (100)^3\text{ cubic centimeters}}\)

3. SIMPLIFY to find the cubic conversion factor

• Calculate \(\mathrm{(100)^3 = 100 \times 100 \times 100 = 1{,}000{,}000}\)
• So: \(\mathrm{1\text{ cubic meter} = 1{,}000{,}000\text{ cubic centimeters}}\)

4. SIMPLIFY the final conversion

• Convert the given volume: \(\mathrm{4\text{ cubic meters} \times 1{,}000{,}000\text{ cubic centimeters per cubic meter}}\)
• \(\mathrm{4 \times 1{,}000{,}000 = 4{,}000{,}000\text{ cubic centimeters}}\)

Answer: D. 4,000,000

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students treat volume conversion like linear conversion, simply multiplying by the linear factor instead of cubing it.

They reason: "\(\mathrm{1\text{ meter} = 100\text{ centimeters}}\), so \(\mathrm{4\text{ cubic meters} = 4 \times 100 = 400\text{ cubic centimeters}}\)." This completely misses that volume requires a cubic relationship.

This leads them to select Choice A (400).

Second Most Common Error:

Partial INFER reasoning: Students recognize they need to do something more than linear conversion, but incorrectly square the conversion factor instead of cubing it.

They calculate: \(\mathrm{4 \times (100)^2 = 4 \times 10{,}000 = 40{,}000}\), treating it like area conversion rather than volume conversion.

This leads them to select Choice B (40,000).

The Bottom Line:

The core challenge is recognizing the dimensional relationship - volume scales with the cube of linear dimensions. Students who miss this fundamental insight about how units transform will apply the wrong conversion factor entirely.