A student estimates the volume of air in a classroom. Describe how the student could make a reasonable estimate of the volume of air in the classroom, and explain how they decide whether their answer is a sensible order of magnitude.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Estimating physical quantities is an important skill in physics. A typical classroom is used as an example.
Model answer (5 marks)
1. Approximate the classroom as a cuboid (rectangular box).
2. Estimate the three dimensions: length, width and height. For example, length ≈ 10 m, width ≈ 8 m, height ≈ 3 m.
3. Calculate the volume by multiplying the three estimates: V ≈ 10 m × 8 m × 3 m = 240 m³.
4. Check the order of magnitude by comparing the result to a familiar quantity, e.g. a typical 200 m³ swimming pool or a 100 m³ bus.
5. Conclude that 240 m³ is a sensible estimate because it lies in the hundreds of cubic metres, which is the expected order of magnitude for a classroom.
2. Estimate the three dimensions: length, width and height. For example, length ≈ 10 m, width ≈ 8 m, height ≈ 3 m.
3. Calculate the volume by multiplying the three estimates: V ≈ 10 m × 8 m × 3 m = 240 m³.
4. Check the order of magnitude by comparing the result to a familiar quantity, e.g. a typical 200 m³ swimming pool or a 100 m³ bus.
5. Conclude that 240 m³ is a sensible estimate because it lies in the hundreds of cubic metres, which is the expected order of magnitude for a classroom.
Examiner tips
- Use the command word ‘describe’ to list steps in order; include the cuboid assumption and dimension estimates. Show the multiplication and a comparison to a known quantity. Keep the answer concise and use UK spelling.
Common mistakes
- Failing to state the cuboid approximation or omitting one of the three dimensions. Giving an unrealistic dimension (e.g. 50 m height) leading to an incorrect order of magnitude. Not comparing the result to a known quantity to justify the estimate.
Mark scheme (5 marks)
- Identifies that the classroom can be approximated as a cuboid (or rectangular box)
- States that length, width, and height of the room must each be estimated
- Gives a reasonable estimate for at least one dimension (e.g. length 8–12 m, width 6–10 m, height 2.5–4 m)
- States that volume is calculated by multiplying length × width × height
- Explains that the estimate is sensible if it is the correct order of magnitude (e.g. hundreds of cubic metres, not thousands or tens), by comparing it to a known quantity or everyday experience
Key terms in this question
Related
- All AQA A-Level Physics (7408) revision notes →
- How to answer a "Describe" question →
- Decode the mark scheme abbreviations →
More Estimation of Physical Quantities questions
- A student wants to estimate the power output of a person walking up a flight of …
- A student wants to estimate the gravitational potential energy stored in a full …
- A student wants to estimate the kinetic energy of a cyclist travelling along a f…
- Explain how a student could estimate the volume of a human lung, giving a reason…
- Explain how a student could estimate the speed of a car travelling along a road,…
- A student wants to estimate the time it takes for a human heart to beat once. Ex…