To study fluctuations in composition, samples of pumice were taken from 29 locations and cut in the shape of a...

1. TRANSLATE the problem information

• Given information:
  • Shape: cube made of pumice
  • Edge length: 3.000 centimeters
  • Density: 0.230 grams per cubic centimeter
  • Find: mass in grams

2. INFER the solution approach

• To find mass, we need to use the density relationship: \(\mathrm{mass = density \times volume}\)
• Since we have density but not volume, we must calculate the volume first
• For a cube, volume depends on the edge length

3. SIMPLIFY to find the volume

• \(\mathrm{Volume\ of\ cube = edge^3}\)
• \(\mathrm{Volume = (3.000\ cm)^3 = 27.000\ cm^3}\)

4. SIMPLIFY to find the mass

• \(\mathrm{mass = density \times volume}\)
• \(\mathrm{mass = 0.230\ g/cm^3 \times 27.000\ cm^3 = 6.21\ g}\)

Answer: 6.21

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize they need to calculate volume first before they can find mass. They might try to use the edge length directly with density, leading to an incorrect calculation like \(\mathrm{0.230 \times 3.000 = 0.69}\). This leads to confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify they need volume, but make arithmetic errors in cubing. They might calculate \(\mathrm{(3.000)^3}\) incorrectly, getting values like 9 or 18 instead of 27. This propagates through to give wrong final answers like 2.07 or 4.14, causing them to get stuck and randomly select an answer.

The Bottom Line:

This problem tests whether students can connect multiple concepts in sequence - they need to recognize that density problems often require calculating volume first, then apply that volume correctly in the density formula. The straightforward calculations can mask the underlying conceptual reasoning required.