To study the moisture content in a group of trees, samples from the trunk of each tree were taken from...

1. TRANSLATE the problem information

• Given information:
  • Edge length of cube: 2.00 centimeters
  • Mass of cube: 2.56 grams
  • Need to find: density in grams per cubic centimeter

2. INFER the solution approach

• To find density, we need both mass and volume
• We have mass, but need to calculate volume first
• Since it's a cube, we can use the volume formula \(\mathrm{V = s^3}\)

3. SIMPLIFY to find the volume

• Volume of cube = \(\mathrm{s^3 = (2.00\text{ cm})^3 = 8.00\text{ cubic centimeters}}\)

4. SIMPLIFY to calculate density

• Density = mass/volume = \(\mathrm{\frac{2.56\text{ grams}}{8.00\text{ cubic centimeters}}}\)
• Density = 0.32 grams per cubic centimeter (use calculator)

Answer: 0.32 grams per cubic centimeter

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students often don't recognize that finding density requires a two-step process. They might try to use the given numbers directly without realizing they need to calculate volume first.

This leads to confusion about what formula to use and causes them to get stuck and guess randomly.

Second Most Common Error Path:

Conceptual confusion about cube volume: Some students might confuse the volume formula, using \(\mathrm{V = s^2}\) (area) instead of \(\mathrm{V = s^3}\) (volume), or forget to cube the edge length completely.

Using \(\mathrm{V = (2.00)^2 = 4.00}\) instead of 8.00, they would calculate density as \(\mathrm{2.56/4.00 = 0.64}\), leading to an incorrect answer.

The Bottom Line:

This problem tests whether students can break down a multi-step problem systematically. The key insight is recognizing that density problems always require both mass and volume, and when volume isn't given directly, it must be calculated first using geometric formulas.