Worked exercise — Bananas to feed the Italian population

Problem

If every Italian ate one banana a day, how many tonnes of bananas would Italy need in a year?

Solution

Step 1 — Estimating the data. Let’s set up a Fermi estimate with a few common-sense figures:

• Italian population: $\sim 6\cdot 10^7$ people;
• Days in a year: $\sim 365$;
• Mass of a banana: $\sim 0{,}12\;\text{kg}$.

Step 2 — Total annual mass. The overall mass is the product of the three factors:

$M = 6\cdot 10^7 \cdot 365\cdot 0{,}12 \approx 2{,}6\cdot 10^9\;\text{kg}$

Step 3 — Conversion to tonnes. Since $1\;\text{t} = 10^3\;\text{kg}$:

$\ev{M \approx 2{,}6\cdot 10^6\;\text{t} \approx 2{,}6\ \text{million tonnes}}$

Links

Topics: Physical quantities and measurement Concepts: Scientific notation and orders of magnitude Skills: Fermi estimates