An object is composed of a material with a density of 15 grams per cubic centimeter. The mass of the...

1. TRANSLATE the problem information

• Given information:
  • Density = 15 grams per cubic centimeter
  • Mass = 240 grams
  • Need to find: Volume in cubic centimeters

2. INFER the mathematical approach

• Since we have density and mass, we need the density formula: \(\mathrm{D = M/V}\)
• To find volume, we need to rearrange this formula to solve for V
• Rearranging: \(\mathrm{V = M/D}\)

3. SIMPLIFY by substituting and calculating

• Substitute the known values: \(\mathrm{V = 240\ grams ÷ 15\ grams/cm}^3\)
• Calculate: \(\mathrm{240 ÷ 15 = 16}\)
• Therefore: \(\mathrm{V = 16\ cm}^3\)

Answer: B. 16

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students mix up the density formula setup and divide density by mass instead of mass by density.

They calculate \(\mathrm{V = 15 ÷ 240 = 0.0625}\), which doesn't match any answer choice. This leads to confusion and guessing.

Second Most Common Error:

Poor TRANSLATE reasoning: Students correctly identify the density formula but confuse which variable they're solving for, attempting to find mass or density instead of volume.

This causes them to get stuck because they already have the mass and density values, leading them to randomly select an answer.

The Bottom Line:

This problem tests whether students can work backwards from the standard density formula. The key insight is recognizing that when you know density and mass, volume is found by dividing mass by density - not the other way around.