Mixture mass and volume balance Steps:

• Total volume V = 1.00 × 10^{-3} m³; fat volume V_f = 0.040 × V = 4.0 × 10^{-5} m³.
• Fat-free volume V_ff = V - V_f = 9.6 × 10^{-4} m³.
• Fat-free mass m_ff = (1.04 × 10³ kg m^{-3}) × V_ff = 0.9984 kg.
• Fat mass m_f = 1.035 kg - 0.9984 kg = 0.0366 kg.
• Fat density = m_f / V_f = 0.0366 / 4.0 × 10^{-5} = 9.15 × 10³ kg m^{-3}.

Why B is correct:

• Matches the density from the volume-weighted mass balance formula for the milk components.

Why the others are wrong:

• A: Overestimates fat density by ignoring fat-free volume adjustment.
• C: Underestimates by factor of 10 due to volume fraction error.
• D: Too low; assumes incorrect fat-free mass contribution.

Final answer: B