A student is asked to estimate the density of a human body. Explain how the student could arrive at a reasonable estimate, including suitable estimated values for the quantities needed.

AQA A-Level Physics (7408) — 3.1.3 Estimation of Physical Quantities · Explain · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (5 marks)

Density is mass divided by volume. A typical adult weighs about 70 kg. The body can be approximated as a cylinder or a cuboid; a reasonable volume is 0.07 m³ (70 litres). Therefore density ≈70 kg ÷ 0.07 m³ = 1000 kg m⁻³, which is close to the density of water.

Examiner tips

State the formula first, then give the estimated mass and volume, finally calculate the density.
Show the calculation with units to demonstrate understanding of the relationship.

Common mistakes

Using an unrealistic mass (e.g. 200 kg) or volume (e.g. 0.01 m³) leading to a density far from 1000 kg m⁻³.
Failing to show the calculation or omitting units, which loses marks for lack of clarity.

Mark scheme (5 marks)

Recognises that density = mass / volume (or states both mass and volume are needed)
States a reasonable estimated mass for a human body (50–90 kg accepted)
Describes a method to estimate the volume of a human body (e.g. modelling the body as simple geometric shapes such as cylinders or cuboids, or using water displacement)
States a reasonable estimated volume for a human body (0.05–0.09 m³ accepted, or equivalent e.g. 50–90 litres / 50 000–90 000 cm³)
Arrives at a density estimate close to 1000 kg/m³ (accept 700–1100 kg/m³) and/or notes this is close to the density of water

Key terms in this question

density · estimate