Q1.
Estimate how many litres of air you breathe in one day. Start by estimating how many breaths you take per minute, and the volume of one breath. Your aim is not to find an exact answer, but a reasonable estimate.
Answer
About 10,000 litres, or roughly 10 m³ of air a day.
Route 1 — breaths × volume per breath
breathing rate at rest ≈ 12 – 15 breaths per minute
minutes in a day = 60 × 24 = 1440 min
breaths per day = 12 × 1440 to 15 × 1440 = 17280 to 21600
≈ 18 – 22 thousand, say 20 thousand breaths a day
volume of one breath: a party balloon of about 2 litres takes 4 – 5 breaths to fill
so one breath ≈ 2 L ÷ 4 = 0.5 litre
air per day = 20000 × 0.5 L = 10,000 litres
breathing rate at rest ≈ 12 – 15 breaths per minute
minutes in a day = 60 × 24 = 1440 min
breaths per day = 12 × 1440 to 15 × 1440 = 17280 to 21600
≈ 18 – 22 thousand, say 20 thousand breaths a day
volume of one breath: a party balloon of about 2 litres takes 4 – 5 breaths to fill
so one breath ≈ 2 L ÷ 4 = 0.5 litre
air per day = 20000 × 0.5 L = 10,000 litres
Route 2 — the balloon, checked independently
one balloon takes about 20 s to blow up → 3 balloons per minute
(3 balloons / minute) × (2 litres / balloon) × (1440 minutes / day)
= 3 × 2 × 1440 L = 8640 litres per day
one balloon takes about 20 s to blow up → 3 balloons per minute
(3 balloons / minute) × (2 litres / balloon) × (1440 minutes / day)
= 3 × 2 × 1440 L = 8640 litres per day
The two routes give 10,000 L and 8640 L — a difference of about 14%. For an estimate that is excellent agreement, so the answer is trustworthy at the level of “about ten thousand litres”.
Why the cross-check matters: a single estimate can be badly wrong without any warning, because one careless factor of 10 changes everything. Two routes built on different assumptions rarely go wrong in the same direction, so agreement between them is real evidence. Notice also that the two routes are not truly independent — both use the 2-litre balloon — so what the check really tests is the breathing-rate step, and it confirms it. One honest caution: blowing up balloons continuously would exhaust you within minutes, while restful breathing does not, because forced breathing uses far more muscular work than quiet breathing.
Did you know? 10,000 litres is 10 m³ — a box about 2 m × 2 m × 2.5 m, roughly the volume of a small bathroom. The 0.5 litre per breath in this estimate is not a lucky guess either: the tidal volume of a resting adult really is about 500 mL, so the everyday balloon reasoning lands on the medically measured value.