A sample of oak has a density of 807 kilograms per cubic meter. The sample is in the shape of...

1. TRANSLATE the problem information

• Given information:
  • Density of oak sample: \(807\,\mathrm{kg/m^3}\)
  • Shape: cube with edge length \(0.90\,\mathrm{meters}\)
  • Need: mass in kg, rounded to nearest whole number

• What this tells us: We have density and can calculate volume, so we can find mass using the density formula

2. INFER the solution approach

• Key insight: Mass = density × volume, so we need the volume first
• Strategy: Calculate cube volume, then multiply by density, then round

3. Calculate the volume of the cube

• Volume of cube = \(\mathrm{edge}^3\)
• Volume = \((0.90)^3 = 0.729\,\mathrm{m^3}\) (use calculator)

4. SIMPLIFY using the density formula

• Mass = density × volume
• Mass = \(807\,\mathrm{kg/m^3} \times 0.729\,\mathrm{m^3} = 588.303\,\mathrm{kg}\) (use calculator)

5. Round to nearest whole number

• \(588.303\,\mathrm{kg}\) rounds to \(588\,\mathrm{kg}\)

Answer: A. 588

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about density formula: Some students remember the density formula as density = mass/volume but get confused about which form to use. They might try to divide instead of multiply: \(807 \div 0.729 = 1,107\).

This may lead them to select Choice D (1,107).

Second Most Common Error:

Weak SIMPLIFY execution: Students correctly identify the approach but make calculation errors, particularly with \((0.9)^3\). Some might calculate \((0.9)^2 = 0.81\) instead of \((0.9)^3 = 0.729\), leading to mass = \(807 \times 0.81 = 653.67 \rightarrow 654\,\mathrm{kg}\).

This leads to confusion since none of the answer choices match, causing them to guess or recalculate incorrectly, potentially landing on Choice B (726).

The Bottom Line:

This problem tests whether students can correctly apply the density formula in the right direction (multiply, not divide) and perform accurate cube calculations. The key is remembering that when you know density and volume, you multiply them to get mass.